Introduction

In the open field plants experience continuous changes in their physical environment, particularly radiation, water vapor pressure, carbon dioxide concentration, temperature, and wind. These changes in turn affect photosynthesis and transpiration of the plant, with substantial consequences on plant water status and growth. Transients and fluctuations of these various processes assume particular relevance in advancing knowledge on plant response to environmental variables and water deficits and the underlying metabolite and genetic determinants (Caldeira et al. 2014; Morales and Kaiser 2020).

Studies on how photosynthesis and transpiration are affected by these physical variables are most commonly carried out in controlled environments. Often, measurements of gas exchange (water vapor and CO2) are conducted on single plants or leaves in chambers as response to environmental variables, like light (e.g., Liu and van Iersel 2021), temperature (e.g., Brooks and Farquhar 1985), and CO2 (e.g., Stinziano et al. 2017). There are also many studies on communities of single species in controlled environment chambers, either under artificial lighting or sunlight. The conditions in the chambers, however, are altered and do not represent the natural environment.

To study photosynthesis, water vapor flux and energy balance of plant communities in a natural environment, micrometeorological techniques are necessary. Among these techniques, the eddy covariance method is considered to be the desired standard (Baldocchi et al. 1988; Alfieri et al. 2020). To calculate values of fluxes from concentrations of air CO2 and water vapor and temperature and vertical wind velocity by eddy covariance, however, it is necessary to use a long averaging time (usually 30 min) for the measured data (Baldocchi et al. 1988), although the data are generally taken at 10–20 Hz. This makes the resolution of fast responses on a few minutes basis not possible. An alternative way to measure fluxes is the Bowen ratio/energy balance (BREB) technique enhanced with an infrared gas analyzer for the measurement of CO2 gradient (BREB+). Traditionally a long averaging time (e.g., 30 min–1 h) is used also with the BREB + method. However, in an earlier study we evaluated the use of the much shorter averaging time of 5 min for BREB+, and obtained strong evidence (Steduto and Hsiao 1998c) supporting the validity of the results calculated with the short averaging time for canopies of herbaceous crops. This makes it possible to examine on a more realistic time scale the impact of fast environmental variability on fluxes of plant canopies and the consequent changes in water related parameters.

In a previous study using the BREB + technique and the 5-min averaging time (Steduto and Hsiao 1998a), CO2 flux into full maize canopies was found to be tightly linked to photosynthetic photon flux density (PPFD). This is expected but had been rarely clearly observed in the open field because of the long averaging time used for the micrometeorological techniques. In gas exchange chambers, photosynthesis has been shown to be closely (Chazdon and Pearcy 1986) or largely (Schulze et al. 1985; Zhen and Bugbee 2020) linked to fluctuations in PPFD. In the open field, plant water status has been shown to be reduced by sudden increases in radiation, and enhanced by reductions in radiation, as detected indirectly by changes in stem diameter (Namken et al. 1969; Stansell et al. 1973), or in expansive growth (Coster 1927; Wenkert et al. 1978). But transpiration was not monitored at the same time. Changes in transpiration in response to changes in radiation have been observed with relatively artificial systems (e.g., Van Ieperen and Madery 1994; for plants in solution culture).

In a more recent and very illuminating study, Caldeira et al. (2014) concluded that changes in leaf expansive elongation rate as light and evaporative demand change is largely dependent on leaf water status and plant hydraulics, but is obfuscated by hydraulic capacitance. They monitored transpiration by soil water balance taken at intervals of 15 min. In contrast, they measured leaf elongation at 1 min interval. Because the various measurements were carried out separately by different authors with different precisions, some in chambers or green houses, and some in the open field, the relationships among them are uncertain. This study is conducted to assess just how closely these plants processes are linked with each other and to the environment in the open field, with emphasis on radiation. At the same time, the data collected serve to test further the validity of the short averaging time of 5 min for the BREB + technique. To better see the linkages, a number of plant and environmental parameters were measured simultaneously on plants within cotton and sweet corn canopies under conditions of dynamically fluctuating radiation induced by moving clouds, as compared to clear sky conditions. The parameters measured or calculated included photosynthetic photon flux density, net radiation, rate of evapotranspiration, canopy conductance, flux of CO2 from the atmosphere above into the canopy for photosynthesis, air and canopy surface temperature, shoot plus leaf elongation, and change in stem diameter.

Materials and methods

Site and crops

The experiments were conducted at Davis, California, U.S.A., latitude 38° 32’30” N and 18 m above sea level in two sequential years. Cotton (Gossypium hirsutum L. cv. Sure-grow 404, South Centre, AL, USA) was planted on 30 May, 1997, and sweet corn (Zea mays L., cv. Silerrado F1, Harris Moran Seed, Modesto, CA, USA) was planted on 29 June, 1998, in the same large field (4 to 5 ha) on a deep and relatively uniform soil (Yolo silty clay loam), fertilized with 200 kg ha−1 of nitrogen as ammonium sulfate before planting. The soil is fertile and past tests and experience indicated that no other nutrient amendment was needed. For cotton, the field was furrow irrigated 7 days before the planting, and sprinkler irrigated every 10 to 12 days starting 25 days after planting (DAP). The sweet corn field was furrow irrigated every 10 to 12 days starting from 2 DAP. The climate is Mediterranean with high radiation and temperature and little or no rain during the summer.

Micrometeorological measurements

The Bowen-ratio/energy balance/CO2 gradient (BREB+) technique was used to measure evapotranspiration (ET), sensible heat flux (H) and net downward CO2 flux (FCO2) over the field, with the form of energy balance equation being

$$\lambda E={R}_{n}-H-S$$
(1)

where λE energy per unit of time per unit of land area (J m−2 s−1 or W m−2). The rate of ET (in units of water per unit of time per unit of land area, equivalent to depth of water per unit of time) was obtained by dividing latent heat flux with the heat of vaporization of water (λ) at the appropriate temperature. The water equivalent of other energy fluxes was obtained similarly. For the ease of discussion in terms of ET, all energy fluxes are expressed in water depth equivalents (mm h−1). In Eq. 1, incoming energy flux to the canopy/soil surface is taken as positive for Rn, but as negative for H and S. Outgoing energy flux from the canopy/soil surface is taken as positive for λE, H and S.

The BREB(+) system used, not requiring alternation of the upper and lower sensors at regular intervals, has been described in detail earlier (Held et al. 1990; Steduto and Hsiao 1998c). Briefly, Rn was measured with a net radiometer (Q7, Micromet Instruments, Seattle, WA, USA). Temperature differences (ΔT) and vapor pressure differences (Δe) between two heights above the canopy were measured continuously with two triple-shielded ventilated psychrometers capable of resolving temperatures to 0.005 °C. The lower and upper psychrometers was placed, respectively, about 0.3 m and 1.0 m above the cotton canopy, and about 0.7 and 2.1 m above the sweet corn canopy. These positions were within the roughness sublayer, and below the inertial sublayer of the surface boundary layer. In the roughness sublayer the Monin-Obukhov similarity theory is not strictly applicable (Basu and Lacser 2016). Reynolds analogy for similarity of transfer processes between water vapor and heat, however, still holds (Cellier and Brunet 1992), making the Bowen ratio technique valid. This conclusion has been supported by a number of careful experiments (e.g., Demead and Bradley 1985, for forest, and Cellier and Brunet 1992; for maize).

Bowen ratio (β, the ratio of H to λE) was calculated as the ratio of ΔT to Δe multiplied by the psychrometric constant at the appropriate temperature (Jones 1992). S is the mean of measurements made with six or more soil heat flux plates (C.W. Thornswaite Associate, Almer, NJ, USA) buried at approximately 10 mm depth and distributed to be representative of the spatial canopy coverage. Replacing H with β in the energy balance equation, the following equation was obtained and used to calculate λE.

$$\lambda E=\frac{{R}_{n}+S}{1+\beta }$$
(2)

For CO2 flux, the concentration difference in CO2 between the two heights above the canopy (ΔCO2) was measured continuously by drawing air from the upper and lower psychrometer air-intakes, first through a tube containing magnesium perchlorate to remove water vapor, then one stream through the sample cell and the other through the reference cell of an infrared gas analyzer (IRGA, model LI-6252 or 6262, LI-COR, Lincoln, NE, USA) operating in the differential mode. The drift in IRGA zero was corrected for by drawing the same air automatically from the upper psychrometer intake through both the sample and the reference cells every 30 min for 5 min to obtain the zero offset, and deducting the offset value from the measured ΔCO2. As the consequence, the measured CO2 flux had a gap of 5 min for each 30 min interval. In the data presented, this gap was filled by interpolation between the two adjacent data points.

The span of the IRGA was quite stable and was calibrated every two or three days against two tanks of CO2 standard gas, one at 344.5 µmol mol−1, and the other at 327.0 µmol mol−1. By invoking the similarity hypothesis for eddy transfer coefficient for water vapor and CO2, flux of CO2 from the atmosphere into the canopy, (FCO2, in units of micromole CO2 m−2s−1) was calculated as

$${F}_{CO2}=-1.608\cdot E\frac{P\cdot {\varDelta CO}_{2}}{\varDelta e}$$
(3)

where E is the rate of evapotranspiration and P is barometric pressure. As calculated from Eq. 3, ΔCO2 was in units of mass, and was converted to molar quantity by a factor of 1.608 before presenting the FCO2 data.

Simultaneously with the measurement of ET and FCO2, incident PPFD was measured with a quantum sensor (LI-191SB, LI-COR, Lincoln, NE, USA), wind speed was measured with an anemometer 2 m above the canopy, wind direction was measured with a wind vane, and canopy surface temperature (Ts) was measured with an infrared thermometer (Model 4000BL, Everest Interscience INC, Fullerton, CA, USA) with a viewing angle of 15°, positioned toward the north on top of the canopy at an angle 30° from the horizontal. The output from all sensors were scanned at 1 s intervals by a data logger (CR 21X, Campbell Scientific, Logan, UT, USA), averaged every 5 min, and only the mean values were stored. The prevailing wind directions in our field were south, southwest, and north. Rarely did the wind come from the east. The fetch (upwind distance) in the prevailing wind directions for the BREB + system was 190 to 210 m for cotton and 170 to 190 m for sweet corn. The fetch for the west direction was 155 m for cotton and 130 m for sweet corn.

Canopy conductance for water vapor (gcw) was calculated using the Penman-Monteith combination equation (Monteith 1973). The required values for the calculation were λΕ, Rn, S, and Δe measured by the BREB + system, and aerodynamic conductance. Aerodynamic conductance for water vapor (gaw) was calculated from the wind speed data and estimated zero plane displacement (d) and roughness length (zo) (Steduto and Hsiao 1998a). The last two parameters were calculated, respectively, as d = 0.64hc (Cowan 1968) and zo = 0.13hc (Tanner and Pelton 1960), where hc is the canopy height.

Plant elongation and stem diameter change

A linear variable differential transformer (LVDT, 500 h-DC, Schaevitz Sensors, Pennsauken, NJ, USA) was used as position transducer to measure the elongation due to expansive growth of cotton plants in the field. The LVDT was mounted above the apex of the plant (about 0.6 m high) on a thin rod of a metal stand. The tip of a rapidly expanding leaf (approximate 20–30 mm long) at the top of the stem was taped on both sides with two narrow strips of Scotch Magic Tape (3 M Co., St. Paul, MN, USA) longer than the leaf tip width. The tapes extending beyond the tip width were pressed together. A small fish hook, tied to one end of a piece of polyester sewing thread (2 cm long), was hooked through the taped leaf tip. The other end of the thread was tied to the core of the LVDT suspended on a low-tension spring. The LVDT has a maximum linear range of 25 mm and was calibrated with a micrometer (resolution of 6 × 10 –3 mm). The LVDT output was scanned every second with a CR21X data logger. Only the maximum value for each minute was recorded. This was done to minimize errors caused by wind blowing on the plant which reduced the apparent height of the plant sensed as detected by the LVDT. As measured, elongation was that of the stem plus that of the rapidly expanding cotton leaf.

Stem diameter of sweet corn was measured continuously, also with an LVDT (100 h-DC, Schaevitz Sensors, Pennsauken, NJ, USA) in 1998. A bracket was fitted along a lower internode of the stem roughly 200 mm above the soil. The LVDT core was mounted perpendicularly on the stem with its extending end pushing against the stem. The other end of the core was glued to a spring and fastened on the bracket, which includes a V-shaped plastic groove backing the stem against the pushing LVDT core. The position of LVDT core was adjusted so the spring pushed the extending end of the core firmly against the stem, with the core situated in the middle of the linear operation range (5 mm). The LVDT was calibrated with a micrometer, achieving r2 of 0.9998 with 8 observations. LVDT output was scanned every second with CR 21X data-logger and only the 1-min mean data were stored. The rate of plant elongation and of stem diameter expansion and contraction were calculated as 5-point moving averages of the slope of minute-by-minute output, multiplied by the calibration factor.

Results

The focus of this study is on the rapid changes in some plant processes and parameters associated with natural rapid fluctuations in radiation and the consequent fluctuations in transpiration and CO2 flux. As the weather in Davis during the summer is usually clear and clouds appear only when fall approaches, the data for days of variable clouds were obtained in September. For the purpose of reference, we first present some diurnal data for clear days of September.

Canopy CO2 assimilation, ET and stem diameter change on clear days in relations to radiation

The fluxes of energy, water vapor, and downward CO2, along with the photosynthetic photon flux density and air and canopy temperatures, are given in Fig. 1a and b for cotton, and in Fig. 1c and d for sweet corn, for two clear days. The data for cotton were taken on 3 September, 1997 (3/9/1997), with a leaf area index (LAI) of 5.8 and a canopy height of 1.4 m. There was still active leaf growth and no sign of senescence. For contrast, the data for sweet corn were taken on 21/9/1998, at an early senescence stage with a LAI of 4.1 and canopy height of 2.5 m. Both days were clear with bell-shaped diurnal course of PPFD (Fig. 1b and d). The CO2 assimilated by the canopy comes from the atmosphere as well as the soil; so net canopy CO2 assimilation rate is the sum of FCO2 and CO2 efflux from the soil. Soil CO2 efflux was measured by the method described by Steduto and Hsiao (1998b) at intervals of 7 to 10 days and also diurnally. The interpolated daily maximum rates in the early afternoon for 3/9/97 and 21/9/98 were, respectively, 9.8 and 6.3 µmol m−2 s−1. These rates are relatively small compared to the measured FCO2 rates for the major part of the days. Hence, assuming an underestimation of around 15–20% due to soil CO2 efflux, the downward CO2 flux can be taken as a reasonable representation of the canopy assimilation rate. Rates of ET, H and Rn are presented in Fig. 1b and d. For ease of comparison, H and Rn are not given in energy units, but in energy equivalent of mm of water evaporated per hour. Rates of ET are discussed in terms of rates of transpiration because soil evaporation was minimal given the high LAI values and the canopy cover which was 94% for cotton, and 96% for sweet corn. The shaded soil received very little radiation and hence little energy to evaporate water.

Fig. 1
figure 1

Upper panels: Diurnal patterns of downward CO2 flux to the canopy (FCO2), canopy surface temperature (Ts), and air temperature (Ta, measured by the upper Bowen sensor), for cotton (3/9/97) and sweet corn (21/9/98) under sunny sky. Lower panels: Accompanying photosynthetic photon flux density (PPFD), net radiation (Rn), evapotranspiration (ET), and sensible heat flux (H). Open symbols of FCO2 represent measured values, and solid symbols of FCO2, interpolated values for the time during IRGA zeroing. To avoid cluttering, soil heat flux (S), is not given in this and subsequent figures, as very minimal

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For both examples presented in Fig. 1, the maximum FCO2 occurred in the late morning (11:00 or shortly after) prior to the peaking of PPFD. This phenomenon is frequently observed and the possible causes include higher canopy (including stems and reproductive structures) respiration rate due to higher temperature in the afternoon, and reduced stomatal opening due to lower leaf water status (Hirasawa and Hsiao 1999) leading to lower gcw in the afternoon (Steduto and Hsiao 1998a). Maximum FCO2 was approximately 32 µmol m−2 s−1 for cotton, a relatively low rate for that crop, as expected since there was substantial respiration from the load of maturing bolls, moderate temperature and relatively low PPFD because of lateness of the season. Maximum FCO2 was still lower for sweet corn, due largely to the senescent state of the canopy.

The diurnal course of ET, H, and Rn are also given in Fig. 1. The peak value of Rn was 576 and 535 W m−2 respectively, the energy equivalent to evaporate water at the rate of 0.84 and 0.78 mm per hour. The diurnal ET curves were slightly skewed to the early afternoon, consistent with the principle of energy balance, and was caused by the difference in air temperature between morning and afternoon, which in turn altered the flux of H. For the cotton on 3/9/1997, a day with maximum Ta of 31.9 °C, in the morning ET equaled approximately Rn since H was close to zero. ET peaked around noon at about 0.84 mm h−1. In the afternoon, ET exceeded Rn slightly, the result of downward flux of H (negative value in Fig. 1b) from the warm air (Fig. 1a), providing extra energy for ET. In contrast, for sweet corn on 21/9/1998, a cooler day with maximum Ta of 26 °C, maximum ET was only about 0.55 mm h−1, and was substantially less than Rn for most of the day. This was due to the upward flux of H (positive value in Fig. 1d) to the cool air above the canopy (Fig. 1c), reducing the amount of energy available for ET. In addition, the upward flux of H was also due partly to the senescence of the sweet corn canopy. The maximum LAI achieved by the sweet corn earlier was 5.1 and the LAI had declined rapidly from 4.6 on 14/9/98 to 4.1 on 21/9/98.

The maximum canopy conductance for water vapor (gcw), calculated using Penman-Monteith equation, were, respectively, 30 mm s−1 and 16 mm s−1 for the cotton and sweet corn canopy. The substantially lower gcw of the sweet corn may be taken as another indication of reduced stomatal opening and LAI, associated with senescence.

In Fig. 1, there is some inconsistency in the trend in canopy surface temperature (Ts) relative to air temperature (Ta) in terms of the trend in H. Conceptually, H is expected to be upward when canopy is warmer than air, as shown for sweet corn for most of the day, but downward when Ts is cooler than Ta. For cotton, however, between 9:30 and 10:30 Ts was 2–3 °C higher than Ta but H was nearly zero. H became clearly (though slightly) downward after 12:45 but Ts was not cooler than Ta until after 16:00. This discrepancy was probably the result of the infrared thermometer sensing a part of the canopy that was at a higher temperature than the overall canopy. Additionally, canopy age must have played a role as the experimental day was in September while the crop was planted in May.

There was more scatter in the canopy CO2 flux data (Fig. 1a and c) as compared with the ET data (Fig. 1b and d). This was due to the larger random errors associated with CO2 flux calculation in comparison to ET calculation in the BREB + technique (Sinclair et al. 1975; Held et al. 1990). As can be seen from Eq. 3, calculated FCO2 values include measurement errors for CO2 as well as for ET.

Simultaneous with the BREB + measurements, diameter of the sweet corn stem was recorded continuously, and its rate of change (expansion or shrinkage) calculated and presented in Fig. 2. To make comparison easier, also given in Fig. 2 are the ET data from Fig. 1d. The crop was well irrigated. At night and just before sunrise, the stem expanded continuously at a slow rate. Sunrise on that day was around 6:00. Started at around 7:30, 1.5 h after sunrise, the stem started to shrink. The long lag time after sunrise was presumably due to dew formed at night on the foliage surface, as can be seen from the abnormally large ET rate just after the sunrise (Fig. 2), which kept the canopy well hydrated until the surface water evaporated off. The shrinkage rate of the stem then increased along with the increase in canopy transpiration rate, peaking around noon at about 1.4 μm min−1. After that the shrinkage rate slowed gradually, reaching zero after 15:00. Thereafter the stem started to expand, although transpiration at that time was still substantial, about 60% of the daily maximum rate. This is explainable in term of plant water potential gradients and the transpiration rate, as elaborated under Discussion, Sect. 4.1.

Fig. 2
figure 2

Diurnal course of stem diameter change (ΔD) of sweet corn in relation to evapotranspiration (ET) on 21/9/98

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Canopy CO2 assimilation, ET, and sensible heat flux under rapid fluctuating radiation

Examples of the dynamic change of FCO2, ET, and H caused by fast changes in radiation resulting from cloud movements are given in Figs. 3, 4 and 5. In Fig. 3, data are for the cotton field, for the whole day of 2/9/97, and for only the morning of 9/9/97 when there were fluctuations in radiation. On both days the conditions alternated between heavy cloud cover and completely clear sky at intervals of 5 min to 1 h, with Rn and PPFD cut by a half or even two thirds during the cloudy periods. FCO2 on these two days fluctuated in close association with the changes in PPFD (Fig. 3a and d). For the major peaks and troughs, there was very close coincidence between FCO2 and PPFD. Even for the minor peaks and troughs the coincidence was close, when the fact that every sixth value of FCO2 was interpolated (solid circles) because zeroing of the IRGA is taken in account.

Fig. 3
figure 3

Diurnal course of cotton canopy PPFD, FCO2, Rn, ET, H, Ts, Ta, and canopy conductance for water vapor (gcw), on two days (2/9/97 and 9/9/97) of variable cloudy weather. Solid symbols of FCO2 represent interpolated data points. LAI was 5.8 on 2/9/1997 and last irrigation was on 26/8/97. Portion of the day of 9/9/97 when the sky was clear is not depicted. Wind speed on the morning of 9/9/97 was very low and therefore did not permit the calculation of meaningful gcw values

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ET and H fluctuated in close association with the fluctuations in Rn without any apparent time lag (Fig. 3b and e). On 2/9/97, air temperature increased from 17 °C in the early morning to a maximum of just below 30 °C in the late afternoon (Fig. 3c). H was mostly upward (positive) before 10:30, and switched to downward (negative) thereafter as air temperature rose above canopy temperature and provided extra energy for ET. Hence, after 10:30 ET exceeded Rn, particularly in the afternoon. Air temperature was slightly warmer on 9/9/97, and H switched to downward after 11:00 and ET exceeded Rn more noticeably than on 2/9/97. On both days, the sudden reduction in Rn by clouds led to a less upward or more downward flux of H due to sudden cooling of the canopy. Consequently, ET was greater than Rn during periods of intermittent clouds between the sunny periods when air temperature was relatively warm (Fig. 3c and f).

Consistent with the fluctuations in H, canopy surface temperature fluctuated in close association with fluctuations in radiation, without any detectable time lag (Fig. 3c and f). This was probably because heat storage of the plant biomass and air is negligible as compared with day time radiative energy flux (Steduto and Hsiao 1998c). The fast changes in Ts effected by the changes in radiation led to fast changes in vapor pressure difference between the leaf intercellular air space and the bulk air. This was the main reason that fluctuations in transpiration rate followed closely fluctuations in Rn, as already emphasized by Steduto and Hsiao (1998a). Air temperature (Ta) shown in Fig. 3c and f were measured at 1 m above the canopy, where it was still substantially influenced by surface temperature. Air temperature, Ta, also responded to the fluctuation in radiation, but with much smaller amplitudes as compared with Ts.

With each passing cloud, H (Fig. 3b and e) decreased, consistent with the fact that the canopy cooled off faster than the air above (Fig. 3c and f).

The data for the sweet corn field on days of fluctuating in radiation are given in Figs. 4 and 5. The crop was at the grain filling and early senescence stage, with LAI declining from 4.6 on 14/9/98 to 3.8 on 25/9/98. On 24/9/98, the maximum temperature was about 25 °C (Fig. 4c). The day was mainly clear except for three periods of clouds around noon. As the sky alternated between sunny and cloudy, FCO2, ET, and H all followed the fluctuation in radiation closely (Fig. 4a and b). During the periods of sunshine, H was highly positive (outgoing) due to relatively low air temperature and the early senescence, and ET was much less than Rn (Fig. 4b). During cloudy periods, ET was approximately equal to Rn because H was reduced to almost zero due to fast cooling of the canopy with Ts dropping close to Ta (Fig. 4c). On 25/9/98, maximum Ta was only 20 °C (Fig. 5c) and most of the day was cloudy interrupted by short periods of sunshine (Fig. 5a and b). Canopy assimilation fluctuated nearly in unison with fluctuations in PPFD (Fig. 5a). Rn was almost equally partitioned between ET and H (Fig. 5b). In comparison to the day before, this was due to the lower air temperature. Consequently, less Rn was dissipated as ET and more as H after 10:00 compared with 24/9/98 (Fig. 4b).

Fig. 4
figure 4

Diurnal course of sweet corn canopy PPFD, FCO2, Rn, ET, H, Ts, Ta, and gcw as affected by fluctuating radiation on 24/9/98

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Canopy conductance, plant elongation rate and stem diameter change under fluctuating radiation and transpiration

Canopy conductance for water vapor (gcw) calculated with Penman-Monteith combination equation is also presented in Figs. 3, 4 and 5. It is seen that gcw of both cotton and sweet corn fluctuated in close association with major fluctuations in PPFD. This may be expected on the basis of stomatal opening and closing in response to PPFD, as well documented with leaf chambers (e.g., Knapp 1993), but has rarely been observed before at canopy level in open field because of the long averaging time used in common micrometeorological measurements. The lower transpiration and higher upward sensible heat flux for sweet corn (Figs. 4 and 5) as compared to cotton (Fig. 3) were related partly to their gcw. Canopy conductance was substantially lower for sweet corn (Figs. 4c and 5c) than for cotton (Fig. 3c), largely the result of more advanced senescence of the sweet corn canopy, as indicated by the decline in green leaf area. In the early morning of 24/9/98, the calculated gcw (Fig. 4c) was spuriously high, as a result of dew evaporating from the foliage. Later up to 11:00, gcw oscillated with no apparent cause. Up to that time, wind velocity was lower than 2 m s−1. In our experience, ET and related parameters measured by the BREB + technique become more noisy under low wind conditions. The significance of changes in gcw and effects on FCO2 and transpiration is elaborated further under Discussion (Sect. 4.3).

Fig. 5
figure 5

Diurnal course of sweet corn PPFD, FCO2, Rn, H, ET, Ta, Ts, and gcw as affected by variable radiation on 25/9/98. LAI was 3.8. Wind speed was around 2.5 to 4.0 m s−1, and last irrigation was on 17/9/98

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On the days of variable radiation, cotton shoot (stem plus leaf) elongation was measured simultaneously. The results (Fig. 6) show a close relationship between elongation or growth rate and transpiration rate. Elongation increased nearly immediately whenever transpiration was suddenly reduced, and decreased nearly immediately when transpiration was suddenly increased. When increases in transpiration were large, there was often shrinkage in the length of the plant, indicated as negative elongation rate in Fig. 6. The large scatter in the elongation data on 2/9/97 (Fig. 6a) was due to relatively high wind (2–3 m s−1) distorting the measurements of plant length. In a few instances, the change in elongation appeared to precede the change in transpiration (e.g. around 9:35 on 9/9/97, Fig. 6b), spuriously. This was the result of measuring ET as 5 min means while elongation was plotted for 1 min intervals.

Fig. 6
figure 6

Elongation rate of cotton shoot (stem + leaf) in relation to ET as affected by variable radiation on 2/9/97 and 9/9/97. Wind speed on 2/9/97 was around 3 to 4 m s−1, and was very low in the morning of 9/9/97

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Stem diameter of the sweet corn was monitored simultaneously on the days of variable clouds. The results (Fig. 7) show sharp changes in stem diameter closely linked to changes in transpiration. On 24/9/97 (Fig. 7a), as the sun rose and transpiration rate increased, the stem began to shrink. For the morning and early afternoon, the stem shrunk most of the time, and the shrinkage rate increased suddenly with sudden increases in transpiration (Fig. 7a). When transpiration was suddenly reduced by clouds, the shrinkage rate was suddenly reduced, to the extent that the shrinkage was reversed and the stem began to expand during the cloudy periods, as happened between 11:00 and 11:40, and between 12:30 and 12:40. Starting around 15:00 in the afternoon, transpiration rate decreased sufficiently to permit continuous expansion of the stem diameter. On 25/9/98 (Fig. 7b), the inverse relationship between transpiration and stem diameter change was even more clear, although the overall shrinkage was less that day because of the more cloudy weather and the generally lower transpiration rates.

Fig. 7
figure 7

Diurnal course of stem diameter change (ΔD) of sweet corn in relation to ET on two days of variable radiation. Time lags (min) in stem diameter change behind some sudden changes in ET are written in (b). Wind speed was around 1.5 to 3.5 m s−1 for 24/9/98, and around 2.5 to 4.0 m s−1 for 25/9/98

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At first glance, one may conclude that the response of expansive growth and stem diameter to changes in transpiration is essentially instantaneous. Close examination of the data, however, revealed some delay in the responses. In the morning the delay time appeared to be about 1.5 min for both growth (Fig. 6) and stem diameter change (Fig. 7b). In the afternoon, the delay time appeared possibly longer. The longest delay time in Fig. 7b was about 8.5 min around 15:30, when plant water status should have been the lowest.

Discussion

Rapid changes in CO2 assimilation and transpiration in response to changes in environmental factors, particularly radiative energy supply, and the subsequent changes in plant water status are expected in theory but not easily observed in crop canopies under field conditions. Only with the demonstration of validity of the short averaging time of 5 min (Steduto and Hsiao 1998c) is it possible to use the non-intrusive micrometeorological BREB + technique to monitor fast changes in canopy fluxes. The 5-min data interval made it possible to view the impact of dynamic changes in radiation on canopy photosynthesis, conductance, temperature and transpiration, and the subsequent effects on shoot elongation and stem diameter change. These changes and causal relations are now discussed and related to background literature.

Shoot elongation and stem diameter change as related to transpiration

The effect of transpiration on plant water status is well known in terms of the long-established concept of soil-plant-atmosphere continuum (SPAC) (Nobel 1999). Plant water uptake is mostly the result of water loss by transpiration; the loss of water mostly from leaves lowers the leaf water potential (Ψ), generating a gradient in Ψ driving water uptake. On days of rapid fluctuating radiation, the effects of changes in transpiration on stem diameter and shoot elongation rate, two parameters intimately tied to plant water status, were dramatic. As shown in Figs. 6 and 7, both processes responded within minutes or sooner to changes in transpiration. The speed of change in these processes as radiation and transpiration changed was most certainly due to changes in plant water status, and too fast to be attributed to changes in photosynthesis and assimilate supply. The direction of change suggested that shoot water status was lowered by increases in transpiration rate and raised by reductions in transpiration rate. Close observations of weather variable indicated that vapor pressure deficit (VPD) of the air and Ta changes had longer gap-time in response to fluctuation in net radiation than shoot elongation and stem diameter changes.

Leaf growth is long known to be a process most sensitive to water stress (Hsiao 1973). In controlled environments, any measurable reduction in Ψ of a growing leaf brought about by reductions in Ψ of the rooting medium caused leaf growth rate to slow, and raising medium Ψ back to the original level caused the immediate recovery in growth (Boyer 1968; Acevedo et al. 1971; Hsiao and Jing 1987). In the laboratory, increases in irradiance on maize plant caused the growth of the young leaves to stop, and reducing the irradiance allowed the growth to resume (Hsiao et al. 1970).

The data here show clearly a close and dynamic relationship between shoot growth (Fig. 6) or stem diameter change (Figs. 2 and 7) and transpiration. In the context of SPAC, these results emphasize the importance of atmospheric conditions and transpiration in addition to soil water status in the determination of plant water status (Schulze 1986) and expansive growth rates over short terms.

Changes in irradiance in the field have long been shown to alter stem diameter (Namken et al. 1969; Klepper et al. 1971). Leaf growth has also been reported long ago to be affected by changes in radiation (Coster 1927; Wenkert et al. 1978). The effect of rapid fluctuations in radiation on stem shrinkage, however, was not clearly seen in the work of Namken et al. (1969) and Klepper et al. (1971), probably due to the coarse resolution of the stem diameter measurements. By measuring net radiation and leaf Ψ every 2 min when clouds passed overhead, Stansell et al. (1973) found that leaf Ψ of cotton increased as radiation was reduced and decreased as radiation was increased within the 2 min measurement interval. Our data demonstrated directly that the response to radiation was due to changes in transpiration rate, and the response in growth and stem diameter was immediate or as quick as within one minute.

These results indicated that plant water status was directly controlled, at least partly, by transpiration which in turn was determined by the radiation load on the canopy.

Canopy photosynthesis in relation to PPFD

Earlier very limited data obtained by Desjardins et al. (1984) with an eddy accumulation technique indicated that 10 min mean CO2 flux into a maize canopy was linked to variations in solar radiation. The present 5-min mean data allowed a more detailed examination of the intimate link. The close dependence of CO2 assimilation on PPFD is particularly obvious on days of variable clouds (Figs. 3, 4 and 5), with FCO2 and PPFD fluctuating in virtual unison, all the way up to levels of full sunlight. Textbooks generally depict leaf photosynthesis to be saturated at PPFD levels substantially lower than full sunlight, especially for C3 species (e.g., Nobel 1999). Nevertheless, for tomato grown in the field under the high radiation environment of Davis, photosynthesis of individual leaves was not truly saturated even at 2.0 mmol m−2 s−1 of PPFD (Bolaños and Hsiao 1991). Similarly, leaf photosynthesis of cotton grown in Davis also increased as PPFD increased from 1.6 to 2.0 mmol m−2 s−1 (Puech-Suanzes et al. 1989). The level of PPFD encountered in this study was certainly not saturating for canopy photosynthesis as is common in many studies (Morales and Kaiser 2020).

When FCO2 of 2/9/97 (Fig. 3) were plotted against PPFD, the relationship (Fig. 8a) is virtually linear up to 2.0 mmol m−2 s−1 of PPFD, but with higher fluxes in the morning than in the afternoon at a given PPFD. Difference between morning and afternoon response to PPFD was also observed or sweet corn for 25/9/1998 (Fig. 9), and also known for cotton canopy measured with a canopy chamber (Puech-Suanzes et al. 1989), and alfalfa canopy measured by the BREB + technique (Asseng and Hsiao 2000).

Possible causes for the morning-afternoon difference have been discussed in Hirasawa and Hsiao (1999). The scatter in the plots of Figs. 8a and 9 are expected since the data were taken over a diurnal cycle with air CO2 concentration, canopy temperature, and wind also varying. Further, stomata, by lagging behind the changes in PPFD, should have had varying effects on photosynthesis, depending on how soon a particular data point was taken after a sudden change in PPFD.

Fig. 8
figure 8

Canopy CO2 flux (FCO2) in relation to incident PPFD in the morning and afternoon (a) and in relation to canopy conductance (gcw) (b) for the cotton canopy field on 2/9/97. Data points represent the period from 7:00 to 17:00 Pacific Standard Time in Fig. 3, with the interpolated points omitted

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Fig. 9
figure 9

Canopy CO2 flux (FCO2) in relation to incident PPFD in the morning and afternoon for the sweet corn canopy field on 25/9/98. Data points represent the period from 7:00 to 17:00 Pacific Standard Time in Fig. 5a, with the interpolated points omitted

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Canopy conductance in relation to PPFD

Canopy conductance responded rapidly to changes in PPFD as clouds moved overhead (Figs. 3, 4 and 5). Although some fluctuations in gcw were apparently not related to PPFD, the nearly hand-in-hand variation in PPFD and gcw is obvious and constitutes a novel observation. Since transpiration was closely linked to radiation, one might expect that transpiration would be highly correlated with gcw, which turned out not to be the case (r2 = 0.31, for 2/9/97). Downward flux of CO2 into the canopy, however, was better correlated with gcw (Fig. 8b, r2 = 0.77). The close link between PPFD and gcw is presumably the result of stomatal movement in response to PPFD.

Stomatal conductance was not measured, however, in this study. The common notion is that stomatal control of gas exchange is lessened as one moves from the scale of individual leaves to that of canopies (McNaughton and Jarvis 1983), and the slower movement of stomata in response to fluctuating irradiance (Yamori et al. 2020) does not match the much faster responses of transpiration, hence the low correlation between canopy conductance and transpiration mentioned above. Regarding the closer correlation with gcw of CO2 flux as compared to water vapor flux, a possible explanation is that the driving gradient for water fluctuates with amplitudes considerably larger than that for the gradient for CO2, mostly because the fast and considerable leaf temperature changes caused by fluctuating radiation. In fact, leaf temperature directly affects saturation vapor pressure of the leaf intercellular space, altering the vapor gradient driving transpiration.

Evapotranspiration in relation to radiation, temperature and sensible heat flux

Earlier ET was demonstrated to be closely associated with net radiation by Pruitt (1964) using a precision lysimeter to measure ET and averaging the data every 15 min. The present 5-min mean data made it possible to examine the relationship between energy or water vapor fluxes and radiation even more closely. As seen in Figs. 3 and 4, and 5, the rise and fall in Rn and ET as clouds moved in and out were in excellent coincidence. There was no detectable lag between them, at least as far as can be determined with a data averaging interval of 5 min. Sensible heat flux also fluctuated in unison. This pattern is consistent with the fact that radiation alters canopy temperature (lower panels of Figs. 3 and 4, and 5), and canopy temperature determines the intercellular water vapor pressure and therefore the gradient in vapor pressure driving transpiration, as already mentioned. Canopy temperature also determines, along with air temperature, the direction and magnitude of the temperature gradient driving sensible heat flux H.

The rate of transpiration for a given radiation environment is substantially modified by H (Baldocchi 1994). For well-watered crops in the semi-arid climate of Davis, California, during the summer season prior to senescence, H is usually upward (positive) in the morning, carrying energy away from the canopy, and turns downward (negative) later in the day as air temperature rises, supplying energy to the canopy (Fig. 1b; Steduto and Hsiao 1998a). Thus, ET is higher in the afternoon compared to the morning for a given net radiation flux. On cooler days, H tends to be more upward, and vice versa for warmer days. In this study, H for the sweet corn followed the morning upward and afternoon downward pattern (Xu 2000) until autumn approached and the crop began to senesce. Then H became less negative or even substantially positive and ET became substantially less, the result partly of cooler air temperature, and partly of lower gcw. For example, the maximum gcw for the sweet corn on 21/9/97, a clear day with H upward most of the time, was 16 mm s−1 (legend, Fig. 1), compare to 20 to 25 mm s−1 for clear days before senescence (Xu 2000). At 16 mm s−1gcw was low enough to begin exerting substantial control over ET (Steduto and Hsiao 1998b). In spite of the low gcw, air temperature still played a role. Air temperature was substantially higher on 24/9/98 (Fig. 4c) than the day after (Fig. 5c). As the consequence, there was less upward H and more transpiration (Fig. 4b vs. Figure 5b) on 24/9/98.

Time lag in responses of elongation and stem diameter to changes in transpiration

As mentioned, there was often a slight delay in the response of growth (Fig. 6) and stem diameter (Fig. 7b) to changes in transpiration rate. This delay was 1 to 2 min early in the day but appeared to lengthen in the afternoon (Fig. 7b). Although growth and stem diameter were measured for 1-min intervals, the delay time could not be determined more definitively because transpiration rates were averaged for periods of 5 min. The delay is explainable in terms of water storage capacity or capacitance (change in water volume per unit of change in Ψ) of the plant Ψ. At high turgor pressure (hence high Ψ), water capacitance is low because a decrease in relative water content (RWC) of the tissue brings about a drop in pressure potential in addition to the drop in solute (osmotic) potential. As turgor pressure decreases, its decrease per unit of decrease in Ψ becomes less because cell walls become less taut. So, canopy foliage in early afternoons, at or near the lowest Ψ, has higher water capacitance, resulting in longer lag time.

When transpiration changes suddenly, Ψ of leaf cells changes quickly in response because the rate of water loss is changed while uptake into cells continues momentarily as before, driven by the existing Ψ gradient that changes more gradually after the perturbation due to water capacitance. Once changes in cell Ψ are transmitted to the veins in the leaf, changes in tension in the leaf xylem are transmitted throughout the xylem system as pressure waves travelling by the speed of sound, with modulation by capacitance along the way. Because wall of the xylem is reinforced by secondary thickening, it is very low in elasticity and hence, capacitance is very small. Therefore, propagation of changes in Ψ is nearly instantaneous in the xylem system, but much slower from cell to cell, as indicated by the difference in half time for pressure equilibration for the two locations (Frensch and Hsiao 1993). On this basis, the 1–2 min of delay in the response of shoot elongation and stem diameter to fluctuations in transpiration probably reflected the relatively large capacitance of the parenchyma cells.

Using extensive data obtained with phenotyping platform, Caldeira et al. (2014) evaluated the causal sequence of plant events elicited by rapid changes in evaporative demand and root water supply. They focused on leaf elongation rate, transpiration, and plant hydraulics but also included changes in gene transcripts for expansive growth and membrane permeability. Caldeira et al. (2014) found leaf elongation rate to respond to environmental changes with a half time in the order of 30 min, versus 1 to 2 h for transpiration and leaf water potential. With a model that accounts for changes in plant hydraulics and water capacitance, they concluded from simulations that nevertheless leaf elongation changes is the direct result of changes in water status, mainly brought about by stomatal response to radiation and the resultant change in transpiration. Our results are largely consistent with their findings, with a couple of exceptions. The first is that the initial change in transpiration to rapid radiation fluctuation, taking place in 1.5 min or less, is the result of quick change in leaf temperature, altering the water vapor gradient driving transpiration. Although stomata respond to radiation quickly, significant change in stomatal conductance would require more than a couple of minutes. The other exception is that because we monitored at much shorter time intervals, we found the responses to be in terms of one or two minutes, much faster than the time they specified.

Further validation of the short averaging time of 5 min for the BREB + technique

This study provides additional data supporting the use of the short averaging time of 5 min for the BREB + technique. Much of our discussion has been centered on the hand-in-hand fluctuations in assimilation and transpiration with fluctuation in radiation.

Because Rn enters into the calculation of ET (Eq. 2) and of canopy assimilation (Eq. 3), however, the question of whether the close links among these parameters were the result of autocorrelation must be addressed. In the original paper validating the 5-min averaging time, Steduto and Hsiao (1998c) presented several lines of evidence to largely rule out autocorrelation as a factor. The evidence included the fact that fluctuations in Ts, measured independently, was consistent with the calculated fluctuations in ET. More extensive Ts data (Figs. 3, 4 and 5) is presented here to strengthen that argument. More importantly, two additional independently measured parameters, shoot elongation rate (Fig. 6) and stem diameter change (Fig. 7), were found to fluctuate in coincidence with the calculated fluctuations in ET. Fluctuations in transpiration is expected to have immediate impact on elongation and stem diameter through its effect on tissue water status. As for assimilation, the rapid response of photosynthesis to and dependence on PPFD are well established in numerous studies under conditions more controlled than that of the open field. These results, taken together, indicate strongly that the rapid changes in fluxes measured by the BREB + technique are real and not the result of autocorrelation.

The dynamic fluctuations in photosynthesis, growth, and plant water status and temperature on days of fluctuating radiation would appear to require rapid adjustment in molecular processes underlying the trafficking of resources and coordination of growth in planta (Slattery et al. 2018). Caldeira et al. (2014) summarized and evaluated a number of metabolic and gene related changes, including transcripts for aquaporin and hormones, for their relative speed of response. They found them to be considerably slower than the leaf elongation response.

This study clearly shows that rapid fluctuations in radiation elicit similar rapid responses in expansive growth and cgw, via fluctuations in ET which, in turn, induces fluctuations in plant water status. However, the complex interplays between the naturally varying physical environment and the molecular events underlying plant overall performance await further elucidation, best with measurements taken at very short intervals. This study further demonstrates the validity of short averaging time (5 min) of the Bowen-Ratio Energy Balance micrometeorological method.