Measurement of Cotton Transpiration

There are a few field methods available to directly measure water evapotranspiration (ET) along with its two components, evaporation from the soil (E) and from the crop (T). One such technique that measures T, uses sensors to calculate the sap flow (F) of water through the plant stem and is based on the conservation of mass and energy, i.e., the stem heat balance method. This in-strument consists of a flexible heater that is wrapped around the plant stem with temperature sensors to measure the difference in temperature of F below and above the heater. This is a null method, where all inputs and outputs are known and the calculated F is a direct measure of T. This method has been used to measure T in a variety of crops, including cotton, grapes, olive trees, soybean, ornamental and horticultural crops. A new version of the EXO-Skin TM is the Stem Gauge Dual Channel Design (SGDC TM ), which was commercially introduced and had a radically new design resulting in a different energy balance, compared to the original design, which needed experimental verification. An initial evaluation was done with potted cotton (Gossypium hirsutum, L.) plants in a greenhouse experiment showing that values of cotton-T measured with the new sensor were accurate; however, this comparison was limited to daily T < 2 mm/d. Thus, our objective was to expand the initial line was significantly different than 1 and if the intercept was significantly different than 0. Pooling all data yielded an almost 1:1 relation between values for a daily transpiration range from 2 to 7 mm/d. We concluded that the new sensor provides a robust and direct measure of hourly and daily cotton-T for a wide range of environmental conditions.


Introduction
Evaporation of water from a crop involves losses of water from the soil (E) and from the plant (T) and under field conditions the most accurate measurement of evapotranspiration (ET = E + T) is gravimetric by using weighing lysimeters [1] [2]. The partitioning of ET into its two components usually involves the direct measure of ET and of either E or T and may include simulation models to calculate the values of E, T, and ET throughout the growing season [3] [4]. Nevertheless, an independent measure of any two of the three terms, i.e., E, T and ET, are needed as the unknown value can then be determined by difference. The direct measure of T under field conditions is a challenge and knowledge of this value throughout the growing season is important to manage both irrigation and plant productivity [4] [5]. Further, knowledge of T can also be used to evaluate the water use efficiency of a cropping system by determining the crop yield per unit of T [4] [5].
The direct measurement of ET under field conditions can be done by a variety of methods that include stem flow gauges [6] [7] [8], growth chambers [9] [10] [11], weighing lysimeters [1] [2] [12], and micrometeorological methods such as Eddy Covariance [13] [14], and Bowen ratio [15] [16]. Of these methods, and under field conditions only the stem flow gauge is available for routine measurement of T and can also be integrated as a tool for irrigation management [5].
In reality, lysimeters and micrometeorology are field methods mainly used to measure ET, although micro-lysimeters may be used to measure E and T is calculated by difference, i.e., T = ET − E [3] [4].
The measurement of transpiration with stem flow gauges is based on the principles of conservation of mass and energy and it is considered a null method, i.e., all inputs and outputs are known. The sensor operates by applying a known amount of heat via a flexible heater that surrounds the stem that is well insulated.
The method of operation is known as the Stem Heat Balance (SHB) as given by [6] [7]. The SHB method has been extensively used and tested in a variety of agricultural crops, e.g., in grapes by [17], in olive trees by [18], in woody plants by [19], in cotton by [8] [20], and soybean by [21] [22], as well as on other crops. The general consensus is that the SHB method provides a direct and accurate measure of plant T.
The SHB as given by [6] was used to design stem flow gauges patented in 1993 and 1994, by [23] [24] and sold by a commercial company (Dynamax Inc., Houston, TX, USA). In 2013, a new patent was filed [25] introducing a new design of a stem flow gauge but still based on the SHB. The new design included a different heater, insulation material and wire positions for thermocouples. Further, the location and number of thermocouples were grouped to make fewer connections and a more accurate differential temperature to calculate water flux temperature increase. The new sensor was named the Exo-Skin TM SGDC TM Sap Flow Sensor [25] and as pointed by [8] there were significant changes from the original stem flow gauge design that warranted experimental verification of T meas-  [28]. However, installation is expensive and requires maintenance that is laborious, which adds to the cost of operation. Conversely, growth chambers provide an alternative and less expensive method to measure whole plant ET under field conditions. Field growth chambers may be a fixed structure or portable and are classified as either open or closed systems [9]. Open systems measure the canopy gas exchange of CO 2 and H 2 O from the difference between the input and output of gas concentrations through the chamber. In a closed system, water transpired raises the chamber humidity and this water is condensed, usually on chilled, refrigerated coils, to maintain a specific humidity set point. The water removed is T or ET depending on operational procedures [29]. Therefore, of the three available methods we selected portable growth chambers of the type designed and tested by [9] [10] [11] to measure whole plant canopy T.
The objective of this work was to expand our initial test [8] and evaluate the

Materials and Methods
Herein, we present a follow-up of the initial evaluation of a new stem flow gauge sensor described by [8]. For additional and detailed information, the reader is referred to the patent describing the new stem flow gauge [25], and to the design of the growth chambers [9] [10] [11].

Field Experiment
The  [10] were used in our experiments. In this experiment, air was pushed through the system and air flow rate was measured at the entrance. The advantage of pushing the air through the chamber system is that this causes a slight positive over-pressure inside the chamber and thus eliminates the need for sealing the soil surface with a plastic barrier to prevent soil gases (including water vapor from the soil) from contaminating the chamber atmosphere and over estimating T. In previous experiments with these chambers, air was pulled through the chambers with the soil surface tightly sealed [9] [10]. The three chambers were placed on East, Central and West locations within the experimental plot, at ~5 m apart from each other. In each chamber, we installed four stem flow gauge sensors (SGDC-7 and SGDC-10 Exo-Skin TM Sap Flow Sensors, Dynamax, Houston, TX) on individual cotton plants. The sap flow sensor installed depended on the stem diameter as measured with a micrometer caliper. The two models of sap flow sensors used accommodated stem diameters between 6.5 and 13 mm. The sensors were installed following guidelines given by Dynamax as shown in a video (http://www.dynamax.com/technical-center/videos-and-tutorials/transpiration-s Agricultural Sciences ap-flow) and as described by [8]. The

Stem Flow Gauge Sensor
In this section we give a brief description on the principles of operation of the The energy balance of a heated stem is given by the following equation: where P is the power (heat flux) applied to the heater, q a is the axial heat loss, q r is the radial heat loss, q c is the convective heat loss, and S is a storage term. The axial heat loss q a has an upward (q u ) and downward (q d ) flow of heat along the axis, such that q a = q u + q d . In general and for small plants, the magnitude of S is small compared to other terms in Equation (1) and thus assumed to be zero. An exception to this rule is when the SHB is used to measure the T of large trees [31]. All terms in Equation (1) have units of power, W.
The new sensor is based on the SHB method and due to a modification on the placement of thermocouples to measure the differential temperature (dT) resulted in a different energy balance equation compared to the original design.
An example of several thermocouples threaded with constantan copper wire and used in the new design is shown in figure 2 in [8]. This is an example of a sensor that can accommodate plant stems within a 9 to 13 mm diameter, i.e., model SGDC-10 [25]. In the new design, the measurement of a single and averaged value of the difference in temperature of the sap flow above and below the heater, dT u,d is read by one channel, eliminating the need to individually calculate the vertical axial conduction (q a ), with its upward (q u ) and downward (q d ) flow of heat. Significant is that the thermocouples are angled to the stem tangent and measure the two opposite sides of the heated axial temperature rise, and thus these measurements are more representative of the temperature increase.
Another result of the thermocouple placement is that all energy losses by conduction are grouped into a single value of q c , which is calculated from the radial thermopile representing all heat conduction in and out of the stem. The thermopile signal is the second of the two channels in the Dual-Channel SGDC TM design. It has been shown [25] that in the new sensor the axial (q a ) heat loss was about 10% to 20% of the radial (q r ) heat loss, and that when the two variables were combined into a single variable q f = q a + q r , lead to a valid energy balance with only two terms compared to Equation (1), as follows: As with the previous sensor design, the sheath conductivity (K sh ) was calculated assuming that the flux of water through the stem is zero at dawn and is calculated by: where E is the input emf voltage (V) from the thermopile. In the new sensor, heat from conductivity is all derived from radial flow including any increase in K sh due to the grouping of q a and q r into a single variable. By design in the new sensor the higher K sh means that the vertical (axial) heat conduction q a is included in q c , resulting in a representative conductance term in the energy balance. Therefore, dT (˚C) is calculated from the average temperature (A h and B h in mV) measured with two thermocouples (type T-thermocouple, converted with 0.040 mV/˚C) as: The sap flow through the stem (F) as measured with the new sensor reduces to: where F is the mass flux of water (kg/s), and C p is the volumetric heat capacity of water (J/kg ˚C). This equation shows that the flow of water through the stem is calculated from three parameters: the power provided by the heater (P), the convective heat loss (q c ) and the average difference in temperature above and below the heater (dT). The calculation of F in the new design is a drastic simplification of the calculation of F for the original design as given by Equation (6) in [8]. Added simplification is that P, the power input, was measured as the input These values represent the normalized transpiration per unit leaf area [20].
The average plot LAI was calculated from the average measured leaf area of all cotton plants in each of the three CETA chambers as given by [20]. To do so we

Growth Chamber
We used chambers designed and tested by [9] [10] [11]. These chambers were designed to monitor whole canopy carbon dioxide and water fluxes of crop fields and are known as CETA chambers, which is an abbreviation for Canopy Evapo- The transpiration from the canopy T was obtained by combining Equation (6) with Equation (7) and rearranging terms as follows: As with the stem flow gauges the T between 9:00 PM and 6:00 AM was assumed to be zero and cotton-T was expressed on a leaf area basis using the measured leaf area data from the final destructive sample. Further, the value of cotton-T measured with the CETA chamber includes the evaporation of water from the soil (E). However, this value is small, i.e., E  T, as shown by [3] for a cotton crop in the Texas High Plains. Further, E in the chamber is minimized by pushing air through the system creating a small overpressure. Also, during the measurement period the majority of the soil surface remained dry except for the area surrounding the drip emitter immediately after irrigation. There are only two environmental setpoints used in the CETA chambers. The first one is the CO 2 enrichment setpoint that is not applicable as it was not used in this study [11]. The second setpoint, is the air flow rate through the chamber [9]. A faster air flow rate is set for daytime hours and a slower rate is set for nighttime periods as suggested by [11]. In either case the average flow rate through the chambers is given as moles of air adjusted for temperature in the gas exchange equations. Also, we have a variable flow rate in m 3 /s calculated and recorded by the data logger, that when divided by the CETA chamber surface area (0.75 m 2 ), gives the air flow rate in m/s inside the CETA chamber.

Results and Discussion
The experimental results comparing measured values of cotton-T obtained with the Exo-Skin TM SGDC TM Sap Flow Sensor and CETA growth chambers are given for hourly and daily values across the 16-day period, from DOY 245 to 259, 2017. The initial evaluation was given by [8] where cotton-T values were compared for daily T < 2 mm/d.   [3]. To accommodate the measured range of stem diameters (7.9 -11.5 mm) we used two models of the Exo-Skin TM Sap Flow Sensor, i.e., the SGDC-7 and SGDC-10.
The main objective of this experiment was to evaluate the Exo-Skin TM SGDC TM Sap Flow Sensor to measure cotton-T for typical daily values in the 4 -7 mm/d range [5]. For this purpose, we compared hourly and daily values of cotton-T measured with the Exo-Skin TM SGDC TM Sap Flow Sensor to values measured with the CETA chambers. The t-test comparison, between the two values, showed no difference of slope and intercept (p > 0.05) and thus all measured data were pooled and the intercept was forced through the origin, i.e., y = m(x). A summary of the linear regression analysis comparing hourly values of cotton-T measured with the stem flow gauge sensor and chambers are given in Table 2.
A plot of pooled data, from all three CETA chambers, of hourly cotton-T obtained with the stem flow sensor as a function of the corresponding measured value obtained with the CETA chamber is given in Figure 1. Also shown is the standard deviation of the mean calculated from the four stem flow gauge measurements in each chamber.
Values plotted and shown in Figure 1, indicated no significant differences between the two measured values of cotton-T ( Table 2 Table 2. Linear regression analysis comparing hourly measured values of Exo-Skin TM SGDC TM Sap Flow Sensor T (y) as a function of corresponding measured value for each growth chamber (x) and for pooled data of all three CETA chambers. Given are the number of observations (n), slope (m), intercept (b) and coefficient of determination (r 2 ) for a linear regression (y = mx + b) and when setting intercept to the origin, i.e., to 0, y = mx.  i.e., mm/h, rather than with units of mass flow of water unit time, i.e., g/h, tend to diminish the variability from plant to plant as shown by [8] [17] [20].      [6] provides an accurate measure of cotton-T. The new sensor, compared to the original design, uses less wiring and copper connectors and the number of channels used to record the signal in a data-logger is reduced by 50% [25]. Further, the new design of the stem flow sensor has a different number of thermocouples and their placement to measure the difference in temperature of the sap flow above and below the heater is different from the original design. These modifications resulted in a different energy balance equation used to calculate the sap flow (F) through the stem as given by Equation (5).
An obvious improvement of the Exo-Skin TM SGDC TM Sap Flow Sensor is the flexibility of the heater that gives better contact between the plant stem and the thermocouples used to measure the temperature difference above and below the heater.
Results from this field experiment showed that the measurements of hourly values of cotton-T under field obtained with the Exo-Skin TM SGDC TM Sap Flow Sensor were the same as the values obtained with CETA chambers on the same plants. There were no statistical differences between the two measurements (

Summary and Conclusions
The initial evaluation of the Exo-Skin TM SGDC TM Sap Flow Sensor was conducted on potted cotton plants, weighed with lysimeters, in a greenhouse experiment that resulted in daily values of cotton T < 2 mm/d [8]. We needed to further verify the performance of the new sensors for higher values of daily transpiration and for this purpose we designed a field experiment to measure cot-R. J. Lascano et al.
ton-T using the portable growth CETA chambers designed by [9] [10] [11]. We used three CETA chambers and in each chamber, we installed four Exo-Skin TM SGDC TM Sap Flow Sensor to four of the cotton plants in each chamber. Hourly measurements of cotton-T for a period of 16 days were collected and compared between the two systems. The statistical comparison indicated no significant differences between the two values of measured hourly T, which leads us to conclude that the design of the new stem flow gauge sensor [25] produces robust measures of sap flow, which is a direct measure of transpiration, for a wide range of environmental conditions.
The direct measure of plant T under field conditions is a difficult value to obtain and the Exo-Skin TM SGDC TM Sap Flow Sensor provides a simple and economical method to obtain this value. This new sensor is based on the stem heat balance method given by [6] and the resulting energy balance to calculate the sap flow through the stem is a simplification of the original design. The new sensor requires less wiring and copper connectors and uses 1/2 less channels to record the signal in a data-logger. The flexibility of the heater used in the new design results in better thermal contact with the plant stem and the thermocouples more accurately measure temperature differences above and below the heater.
Results showed that the Exo-Skin TM SGDC TM Sap Flow Sensor provides an accurate measure of plant T as tested with cotton plants in a field experiment for values of T in the 2 -7 mm/d range. Sensors that are based on the stem heat balance method and are used to measure plant transpiration provide an accurate and direct measure of a value that can only be achieved by using large weighing lysimeters. These Exo-Skin TM SGDC TM Sap Flow Sensor provide a tool that can be used for a variety of field applications to optimize irrigation and plant productivity.

Declarations
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