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Instrumentation

Two Algorithms for Variable Power Control of Heat-Balance Sap Flow Gauges under High Flow Rates

USDA-ARS, Horticultural Crops Research Unit, 24106 N. Bunn Rd., Prosser, WA 99350

^* Corresponding author (jtarara{at}wsu.edu)

Received for publication September 1, 2005. The advantages of variable power control for heat-balance sap flow gauges are evident under high flow rates (e.g., >600 g h^–1) where high rates of power must be applied. Under the very high flow rates (e.g., 1500–4000 g h^–1) of mature grapevines (Vitis spp.), we evaluated two algorithms to control the power applied to heat-balance sap flow gauges, and thus the temperature difference (T) above and below gauge heaters: (i) a proportional-derivative (PD) algorithm and (ii) an open-loop controller following the theoretical diurnal course of irradiance. The PD algorithm was tuned for expected maximum flow rates and could keep T within 0.1°C of its daytime (0800–1800 h) target value. Over 21 d, mean daytime T was 1.32 ± 0.001°C (s.e.m.) for an 18-gauge system. 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 daylength. In well-watered vines, the power curve mimicked actual sap flow patterns. As flow rates varied it accommodated the changing dead time of the system, which is the delay or time required before any change in T occurs. Daytime T varied sinusoidally with a typical amplitude of 0.5 to 1.0°C. The coefficient of variation in daytime T appeared to be higher (16–26%) under the open-loop algorithm than under the PD algorithm (5–13%). Under weekly cycles of deficit irrigation, the variance in daytime T increased with the number of days after irrigation, suggesting that the open-loop algorithm might best be applied when the stem energy balance includes an estimate of heat storage.

Abbreviations: D, damping factor • DOY, day of year • G, empirically derived proportional gain factor • K_g, zero-flow gauge conductance • PD, proportional-derivative algorithm