Engineering a sap flow sensor for irrigators Andrew Skinner Measurement Engineering Australia (MEA) Australia Email address:
[email protected]
Keywords: thermal diffusivity, vapour pressure deficit, crop water stress, single probe sap flow sensor, irrigation scheduling, cellular water content Abstract Sap flow sensors designed for irrigators – as distinct from scientific researchers – must be inexpensive and robust, simple to install and interpret, and able to advise a grower when the crop is becoming water stressed. Modern growers also expect data to be delivered to them wherever they may be and whenever they want it, which impacts directly on the sensor energy budget and the costs of transmitting data via radio and web. These stringent demands have prevented sap flow sensors reaching the hands of growers in Australia as a standard irrigation scheduling tool. This paper describes a new approach to using sap flow measurements to allow plantbased scheduling of irrigation. The sensor described does not attempt to make quantitative measurements of sap flow, but relies instead on the fact that is sensitive enough to detect the daily decline of expected sap flow under atmospheric loading as indicated by in-canopy vapour pressure deficit (VPD) measurements. A thermistor probe is inserted into the xylem tissue and forced to dissipate a very precise amount of power (25 mW ± 25 µW), creating a heat field sensitive to both thermal conductivity (enhanced by sap flow) and local heat capacity (affected by cellular water content). The rate of temperature rise monitored by the self-heated thermistor at the centre of this heat field yields a measurement of thermal diffusivity (TD). This low-power transient measurement technique rejects common-mode ambient temperature effects while reporting thermal diffusivity with a resolution of 0.0001 mm2 s-1. Field data collected over three growing seasons in a commercial vineyard in South Australia showed that, in well-irrigated grapevines, morning sap flow enhances thermal conductivity – and hence thermal diffusivity. By contrast, in grapevines under water stress, this sap flow enhanced thermal conductivity disappears. A single ‘crop water stress’ value, measured in hours, was obtained from the daily phase shift between TD and VPD. This phase-shift declined with increasing soil moisture tension down through the soil profile. INTRODUCTION Despite the publication of over 1500 scientific papers1 since the pioneering work of Huber and Schmidt in 1937, sap flow sensors are still not sufficiently simple or robust to have become an everyday tool in use by growers wanting to know ‘when to water’. And despite an ever-deepening understanding of the physiology of plant transpiration mechanisms, no simple method has been described that relates sap flow to crop water stress in a way that farmers can easily apply to more profitably grow their crops. That this is so is no fault of scientists; what has been missing has been an essential layer of specialized engineering. 1
B.R. Loveys, pers. commun.
Unlike scientists – employed largely by universities and public research institutions - engineers are most often employed by private companies. Unlike scientists – subject to the scepticism of their peers to qualify their research – engineers face sceptical farmers when promoting newly-invented irrigation scheduling tools. Unlike scientists whose publication output determines their career advancement – engineers are dependent upon the development of workable and profitable sensors for job promotion by their employers. Unlike scientists – who must build their work upon the published literature – engineers develop instruments based on a considerable store of personal experience and unpublished intellectual property jealously withheld from the public domain by those who pay engineers to acquire it. Unlike scientists – able to access the scientific literature through their institutional libraries – engineers in commercial environments must pay prohibitively expensive prices to access journal articles describing fundamental principles about sap flow and its measurement. Unlike scientists – who seek an understanding of those same fundamental principles – engineers require very long and intensive training in additional technical disciplines to be able to bridge the gap between scientists and growers. Unlike the suppliers of the small numbers of custom-built sap flow sensors in use by the scientific community, designers of instruments for irrigators are bounded by the constraints of low price and high reliability. High development costs must be offset by the expectation of a mass market with lower profit margins. Finally, a ‘new-to-world’ sensor for plant-based irrigation scheduling carries with it the considerable commercial risk of having to educate agents and irrigators alike in the benefits and usage of new technology. For these reasons and more, it is a fragile bridge indeed across the deep chasm between scientists and irrigators; a bridge that can be crossed only by measurement engineers adequately trained in both the academic and commercial worlds and with an unlikely focus on building sensors for use in irrigating horticultural crops. This paper describes a sensor engineered in the forge betwixt science and irrigator. METHODS AND MATERIALS 1. Engineering design issues What, then, are the defining elements of a sap flow sensor suitable for irrigators? Unlike scientists, irrigators have no particular interest in the quantity of water transpired by their crops, but have every interest in knowing when a crop is entering water stress and in need of irrigation (Skinner, 2012). Irrigators then develop a sense of the amount of water to apply based upon the interval between irrigation events, the weather conditions that have prevailed during that interval, and the rate of draw-down of soil moisture reserves. So if ‘crop water stress’ is to be reported to irrigators, sensors need to monitor a plant’s sap flow response with respect to weather conditions. This knowledge must be processed through an algorithm capable of indicating crop water stress (CWS) on a simple scale readily interpreted by irrigators. Additionally, crop water stress sensors must be able to be widely deployed across a single property in order to account for the variability in crop varieties, soil types, irrigation shifts, solar aspect and canopy size. In short, CWS data must be collected inexpensively from dozens of sites across hundreds of hectares and delivered whenever and wherever a farmer may be in near realtime; Australian growers expect web- and mobile-based data delivery. Modern selfhealing mesh radio networks fill this role by transmitting data back to a central Hub that
pushes the data to an automated website from where it can be accessed by the grower, as in Fig. 1. To power these combined CWS, soil moisture and radio systems, energy must be scavenged from the environment where they are located; solar power is an appropriate and proven technology on farms. Both solar and radio systems require the measurement system to be raised on a pole at least two metres above the top of the crop’s canopy. However, the common use of over-row machinery in Australian grape and olive farming operations necessitates the design of a streamlined radio/solar power/sensor system that can be laid down out of harm’s way then re-erected simply once machinery has passed by. This limits the size and shape of the solar panel (Fig. 2), creating one of the most severe bounds on the design of the CWS sensor – it must operate all-year round while consuming less than 40mW of power continuously. Finally, CWS sensors will be installed by irrigation agronomists, not sensor engineers. CWS sensors must therefore be designed to be inserted easily and reliably into plant tissue. 2. Possible engineering solutions The problems outlined above are not scientific problems. They require engineering solutions and appropriate design. While two, three and four probe sap flow sensors have been developed for scientific studies (Smith and Allen, 1996) a single probe sap flow sensor meets the irrigator’s needs for simplicity and robustness. Combining this with a vapour pressure deficit sensor factors in atmospheric loading against which sap flow response and plant cellular recharge can be compared over the 24 hour period between the resting phases of a plant, chosen arbitrarily to be at 6am each morning. The single probe sap flow sensor described in this paper (Fig. 3) is actually a tiny thermal diffusivity probe that is inserted into the xylem tissue of the plant. 3. Thermal diffusivity Thermal diffusivity TD2 is a property of a material that describes its thermal time constant – how quickly its temperature will change in response to a sudden change in heat input. At work are the opposing actions of thermal conductivity (trying to take the heat away) and thermal storage (trying to store that heat nearby). Thermal diffusivity is described in physics as the ratio of these two properties; the thermal conductivity k divided by the material’s volumetric heat capacity ρCp. This is described in the equation (1) ∙
As thermal conductivity k has the units W m-1 ⁰C-1, ρ has the units kg m-3, specific heat Cp has the units J kg-1 ⁰C-1, and one Joule is 1 W s, it can be shown parametrically that thermal diffusivity has the units of m2 s-1. As most materials have thermal diffusivities in the range 1.0 x 10-4 to 1.0 x 10-8 m2 s-1, a more readable unit can be derived by multiplying this small number by 106, giving units of mm2 s-1. We can expect the thermal diffusivity of plant tissue to vary between that of water (0.143 mm2 s-1) and dry wood (0.082 mm2 s-1 for yellow pine). Each sensor used in the field measurements
2 In physics, the Greek symbol α is commonly used for thermal diffusivity, mainly for measurements in substances where no perfusion of water is taking place simultaneously. The initials TD for ‘thermal diffusivity’ have been used throughout this paper for this specific case where sap flow is impinging upon the background thermal properties of the plant tissue.
described in this paper was individually calibrated in agar-gelled water3 and glycerol 4 (0.094 mm2 s-1), so covering a respectable portion of this range. The thermal diffusivity measurement is made by injecting a very precise amount of heat (25 mW ± 25 µW) from a 1.5 mm diameter sphere at the tip of a glass-rod thermistor grafted or drilled into the plant tissue while monitoring the transient (nonsteady-state) response of the sensor’s temperature within the heat field. Typically, the temperature rise of this sensor due to local heat injection is no more than 5 ⁰C above ambient, while the logarithmic portion of this temperature rise that is reliant upon plant tissue properties is no more than 0.3 ⁰C. This narrow operating range places stringent demands upon both the power control and temperature measurement circuits; temperature resolution of better than 0.001 ⁰C allows thermal diffusivity to be resolved to 0.0001 mm2 s-1. The sensor obtains the necessary precision and repeatability by lengthy autocalibration against internal temperature-independent voltage and resistance standards prior to each measurement. To meet grower demands for ‘simpler, more robust and less expensive’ sensors, a single-point TD measurement (Fig. 4) offers significant advantages over the multiple linear probes used in scientific sap flow sensors. This single point heater/sensor also eliminates the spatial temperature gradient errors associated with other thermal diffusivity sap flow sensors such as the Granier sensor (Granier 1985). Furthermore, the differential temperature measurement technique used by the sensor eliminates common-mode background temperatures from the measurement, as this background temperature would rarely vary more than 0.005 ⁰C during the 20 s measurement period. The correct operation of this thermal diffusivity sensor depends upon good thermal contact with the surrounding plant tissue. Poor thermal contact does not damage the sensor, but causes its temperature to rise more than normal as it attempts to push the same amount of heat through a far smaller contact area between sensor and surrounding tissue. The sensor detects and reports this error, which can often be seen in the data set as an ‘inverted’ TD diurnal trace with respect to the VPD signal (which it normally tracks in some rough fashion). 4. Plant water dynamics The effects of plant water dynamics on the thermal diffusivity sensor are two-fold; the sensor is sensitive to both sap flow and tissue water content. Sap flow enhances the ‘effective’ thermal conductivty k of the plant tissue, causing an increase in TD. Heat from the sensor is being conducted away by sap (thermal convection) in addition to the background heat flows in the tissue (thermal conduction). This increase in sap flow is often seen in well-watered plants after sunrise and right up until the warmest part of the day around mid-afternoon before being limited – in most cases – by stomatal closure in the leaves. Sap flow results in the thermal diffusivity signal ‘leading’ the vapour pressure deficit signal that it would normally mimic. This leading TD characteristic has been observed in well-irrigated mature grapevines on a commercial vineyard in December 2011, as in Fig. 5a.
3 ‘Agar-gelled’ water has a ~1% component of agar-gel to ‘jellify’ it without changing the fundamental thermal properties of water; this prevents errors during calibration due to convective heat transport. 4 Glycerol, or glycerine, or glycerin, is a sweet-tasting, colourless, odourless, viscous, low toxicity simple polyol compound widely used in pharmaceutical compounds and readily available. Its high viscosity prevents calibration errors due to convective currents, as in water. When used as a thermal diffusivity calibration standard, the thermal diffusivity of glycerol must be corrected for temperature.
Plant water content changes during the day as plant water status changes. Ever since the work of Klepper et al (1971) scientists have known from dendrometer data that stem diameters shrink during periods of maximum transpiration. As plant tissue recharges and relaxes overnight from the stresses caused by daily transpiration, the tissue density increases and there is a steadily decreasing thermal diffusivity because the component of heat that is being stored by the extra water in the surrounding tissue is increasing. Put another way, changes to the local cell water content change the wood-to-water ratio and hence the tissue density, causing changes in the local volumetric heat capacity. Increasing crop water stress results in the thermal diffusivity signal leading the vapour pressure deficit signal by less-and-less, until TD and VPD are practically in-phase under conditions of crop water stress, as in Fig. 5b. ‘Lagging’ of the TD signal behind the VPD signal has yet to be observed under field conditions, but could conceivably occur if night-time sap flow and cellular recharge – often seen in water-stressed plants or directly after late irrigation – follow days where sap flow is negligible and night-time VPD is high. A more detailed description of field trials of these sensors on a 250 ha commercial vineyard is given by Skinner (2012) 5. Calculating daily crop water stress Each calculation of crop water stress makes use of 24-hours of data (96 x 15-m readings) of VPD versus TD in the period between 6am and 6am. Each TD and VPD point is treated as a vector having magnitude (as measured) and angle (as the time of measurement converted to an angle on a 24-h clock face). The vectors are then broken down into their sine and cosine components to be averaged separately. The resulting 24-h average ‘magnitude’ and ‘hour angle’ are calculated from the Pythagorean Theorem and ‘arctan(sine/cosine)’ formulae of Equations 2 and 3 ∠ tan
∠ tan
∑ !"∙#$ ∙
∑ !"∙ ∙
∑ !"&∙#$ ∙
∑ !"&∙ ∙
% %
(2)
(3)
where t is the time-of-day, expressed as a quarter-hour reading number between 1 (12:00 am) and 96 (11:45 pm). Note that the angle (in radians) that is the result of the computation of the arctan function tan-1 in Equations 2 and 3 is more complex than it might at first appear; this is because spreadsheets treat angles as though they fall in the range +π/2 to –π/2, whereas 24-h angles from midnight to midnight cover the range 0 to 2π. This is resolved by testing the ‘sign’ of the sine and cosine components, such that • • •
if both sine and cosine components are positive, the angle is between 0 and π/2 and is used unchanged if only the cosine component is negative, add π to the angle if the sine component is negative but the cosine component is positive, add 2π to the angle
The conversion from the vector angle (in radians) back to 24-h clock time is performed by
+,-./
'()* ∙ 24 (4) Finally, a measure of ‘crop water stress’ CWS is defined as the angle subtended by these two vectors on the 24-h clock face, and having units of hours 234 ∠ 5 ∠ (5) Crop water stress, as expressed by equation 5, is essentially a measure of how the plant water dynamics – dominated by sap flow – are responding to the atmospheric load placed on the crop by the daily VPD peak. Note that this angular measure is independent of the magnitude of the VPD load, of changing weather conditions and the timing of the VPD peak during the 24-h period. Data from field trials of the sensor in grapevines showed that unstressed vines have a CWS of over 3 hours, and stressed vines have a CWS measured only in minutes RESULTS AND DISCUSSION Fig. 6 shows that crop water stress sensor tracked the average soil moisture tension in the profile with a linear correlation of r2 = 0.95 during the drying phase of one particular grapevine in December 2012. That so little useful data was collected from sensors deployed in the 2011 and 2012 growing seasons had much to do with mechanical failures of the fragile glass-rod thermistors and installation errors due to poor sensor placement in the one-year old vine stems. Some of this uncertainty was removed in the 2013 field trials by placing a more robust cylindrical epoxy TD sensor in the surface xylem layer of the cordon trunk as in Fig. 3. Calibration was also simplified because of the much tighter electrical and dimensional properties of these newer epoxy thermistors. In the 2013 field trails, high-quality CWS and soil moisture sensor data was carried successfully for two months on the sensor-to-web radio network shown in Fig. 1 and Fig. 2 and developed in conjunction with the sensor to provide the daily delivery of CWS data to growers via a web-site. Other scientific questions remain: Where exactly is the sap-conducting tissue in a grape-vine or an apple tree? What is the best way to install the device? What impact does ‘wounding’ have on long-term stability? What are the effects of west-facing branches versus east-facing branches on the TD-VPD phase-shift? What impact do sudden shifts in daily weather patterns have on the diurnal phase-shift reading? Does the sensor work under cool cloudy conditions? CONCLUSIONS The tiny amount of useful data gleaned from this field work suggests that there is a strong correspondence between soil moisture conditions and a single daily number representing crop water stress. Larger field trials over longer periods in more diverse crops and climates are needed before the CWS sensor can be confidently placed in the hands of irrigators. Such is the long and expensive engineering route between scientific concepts and everyday sap flow tools for growers. ACKNOWLEDGEMENTS AusIndustry (Australia) provided sensor development funding to Measurement Engineering Australia (MEA) with a 2009 Climate Ready grant. Brian Loveys and Everard Edwards of CSIRO Plant Industries contributed much useful advice on plant physiology. Yalumba Wines (Australia) provided open-access to their Oxford Landing vineyard for trial work in testing both the sensors and their associated radio network.
LITERATURE CITED Granier, A. 1985. Une nouvelle méthode pour la mesure du flux de sève brute dans le tronc des arbres. Annales des Sciences Forestières. Vol. 32, p 193-200 Huber, B. and E. Schmidt. 1937. Eine Kompensationsmethode zur thermoelektrischen Messung langsamer Saftströme. Ber. Dtsch. Bot. Ges. 55:514--529. Klepper, B., Browning, D. and Taylor, M. 1971. Stem diameter in relation to plant water status. Plant Physiol. (1971) 48, 683-685 Skinner, A.J. 2012. Field measurements of crop water stress in grapevines using thermal diffusivity and vapour pressure deficit sensors. Seventh International Symposium on Irrigation of Horticulture Crops, Geisenheim, Germany. Acta Horticulturae (in press) Smith, D.M. and Allen, S.J. 1996. Measurement of sap flow in plant stems. J. Exp. Bot. 47(305): 1833-1844 FIGURES
Fig. 1. Sensor-radio mesh networks co-operate to sweep CWS sensor data over wide areas back to a web-connected Hub (shown in the bottom right hand corner of the figure above). These networks are self-healing, in that they find new paths to move data should a node in the network be down as a result of vineyard operations. ‘Hop’ distances of between 1 and 2 kilometers are common in large commercial vineyards.
Fig. 2. Radio field stations need a local energy source (solar power), battery storage, local logging in case of network dropout, and the ability to power and read both CWS and soil moisture sensors. Additionally, such over-row technology must be streamlined (to prevent snagging) and be able to be tilted down out of the path of over-row machinery.
Fig. 3. In the 2013 growing season, robust cylindrical epoxy thermistors were used in place of the glass-rod thermistor sensors used in 2011 and 2012. Their tighter dimensions (1.2 mm dia. x 7 mm long) simplify usage. The thermistor used as a TD sensor is simply pressed into a tight hole drilled into the xylem tissue of the grapevine’s main cordon trunk after the coarse outer bark is peeled away. A reflective insulating pad is placed over the TD sensor to buffer thermal gradients. The in-canopy sensor shelter containing the CWS electronics can just be seen in the top left of the photo.
Fig. 4. Left: the 8-cm cm long polyurethane body of the CWS sensor houses all electronics for powering, auto-calibrating calibrating and measuring the TD sensor (the glass-rod rod thermistor to the bottom bottom-left of the photo) and the VPD sensor (the ‘black spot’ to the right of the sensor body). The radiation shield, normally fitted to prevent radiant heating errors in the VPD sensor, has been removed for clarity. The sensor is i powered and polled on the 3-wire wire SDI SDI-12 bus; this ‘smart sensor’ connection methodology is common in many environmental monitoring systems. Right: cut-away away view of the 12mm long x 1.5 mm diameter glass-rod glass TD sensor thermistor used during the 2011 and 2012 growing seasons, installed by drilling a hole from the centre of an excised petiole across into the conducting xylem tissue at the base of a grape bunch. Nearly all problems experienced in obtaining sensible data from these field trials were as a direct ct consequence of poor placement of this sensor tip in the plant tissue.
Fig. 5. A well-irrigated grapevine (left) shows TD 'leading' VPD by three hours because morning sap flow enhances thermal conductivity, conductivity whereas a water-stressed grapevine (right) shows TD almost 'in-phase' with VPD. VPD. The sap flow signal has almost disappeared for lack of soil moisture.
Fig. 6.. ‘Crop water stress’ versus average soil moisture tension for a one-week one week period when irrigation was withheld. The steady increase in crop water stress corresponds well with the increasingly dry soil conditions. Both soil moisture tension and crop water stress fell off once irrigation was returned on the 25th 25 December 2011.
