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Title: TWO ALOGORITHMS FOR VARIABLE POWER CONTROL OF HEAT-BALANCE SAP FLOW GAUGES UNDER HIGH FLOW RATES

Authors
 Tarara, Julie Ferguson, John

 Submitted to: Agronomy Journal Publication Type: Peer Reviewed Journal Publication Acceptance Date: January 11, 2006 Publication Date: May 2, 2006 Citation: Tarara, J.M., Ferguson, J.C. 2006. Two alogorithms for variable power control of heat-balance sap flow gauges under high flow rates. Agronomy Journal. 98:830-838. Interpretive Summary: It is important to know the amount of water used by various crop plants for a number of reasons: scheduling irrigation, managing plant growth and crop yield, assessing potential effects of various crops on water resources, etc. Scientists often use instruments to measure directly the water use by a small number of plants in a field and then extrapolate this information to larger scales. One such instrument is called a "sap flow gauge" because it measures the flow rate of water, or xylem sap, through the plant stem. The gauge works by applying a small amount of heat to the plant stem, from which the flow of water through the stem can be calculated if certain properties of the stem are known and certain temperatures around the gauge are measured. Use of the gauges is not straightforward for plants that have relatively high rates of sap flow through relatively snall stems, like the trunks of many grapevines. To address these difficulties, we tested two algorithms, or sets of equations, to better control the amount of heat that the gauge applies to the plant stem to avoid overheating the stem while at the same time maintianing accurate estimates of sap flow. The algorithms could be used by any scientist who is familiar with the use of sap flow gauges and who has experience with automatic data loggers. Technical Abstract: The advantages of variable power control for heat-balance sap flow gauges are evident under high flow rates (e.g., >600 g/h) where high rates of power must be applied. We evaluated two algorithms for control of the temperature difference above and below gauge heaters under the extremely high flow rates (e.g., 1500 to 4000 g/h) produced by mature grapevines: 1) a proportional-derivative (PD) algorithm common to process engineering; and 2) an open-loop controller following the theoretical diurnal course of irradiance. The PD algorithm was tuned for expected maximum flow rates and when performing well kept the temperature differnce within 0.1 degrees C of its daytime target value. However, the algorithm was unstable early in the morning and in the evening as rates of sap flow were below those for which the algorithm had been tuned. In the open-loop algorithm, power output was programmed to change according to a sine curve tied to day length. In well-watered vines, the power curve mimicked actual sap flow patterns and thus accommodated the changing dead time of the system as flow rates varied. However, daytime temperature difference also varied sinusoidally, with a typical amplitude of 0.5 to 1.0 degrees C. Under weekly cycles of deficit irrigation, the variance in daytime temperature differnce increased with the number of days after irrigation, suggesting that the algorithm might best be applied when the stem energy balance includes an estimate of heat storage. A running median filter was used to smooth the data from both algorithms, which removed controller-related anomalies and improved cumulative estimates of vine water use but obscured detection of variations in sap flow due to environmental transients.