empirical gradients sap flow methods explained
Various empirical methods have been proposed to extend the limited measurement range of the compensation heat pulse method (CHPM) into the slow and reverse range, and the Marshall-Burgess heat ratio method (HRM) into the high velocity range. The methods are empirical as they require calibrating a derived variable from a traditional CHPM or Marshall-Burgess HRM measurement versus heat pulse velocity (HPV) calculated from CHPM or HRM. Generally, the methods involve finding the average temperature in the downstream and upstream temperature probes (ΔTa) over a specified time period following the heat pulse, and then finding a linear regression between ΔTa and Vc (heat velocity).
Testi and Villalobos (2009) proposed an empirical method to address measurement limitations of CHPM. Termed the Calibrated Average Gradient Method (CAGM), the approach involves, during a normal CHPM measurement cycle, finding ΔTa for 180 seconds following the heat pulse. A linear regression calibration curve is then derived between ΔTa and Vc, as measured by CHPM, only when Vc is in the range between 10 cm/hr to 25 cm/hr. Vc data less than 10 cm/hr can then be calculated via the equation derived from the linear regression analysis.
Testi and Villalobos (2009) derived extremely accurate linear regression curves between ΔTa and Vc when 10 cm/hr < Vc < 25 cm/hr with r2 values of 0.99 and 1.00. However, the linear curves became curvilinear, for reasons unknown to the authors, at values less than ~ -10 cm/hr and greater than 30 cm/hr. Green et al (2009), in a subsequent analysis, found an upper measurement limit for CAGM of 35 cm/hr. Green and Romero (2012) found a running average, centred on a three-day window, provided more accurate results than determining a single curve over an entire growing season. Pearsall et al (2014) found highly correlated values between Vc measurements via CAGM and heat ratio method (HRM).
Another limitation of the CAGM is the possible influence of natural thermal gradients on ΔTa. A shift in absolute temperature during the 180 seconds, where ΔTa are being measured, will affect ΔTa and the accuracy of the linear regression curve (Vandegehuchte & Steppe 2013). Natural thermal gradients can be caused by sudden changes in atmospheric temperature or a sudden increase or decrease of solar radiation on the sensors. How, and the extent to which, natural thermal gradients affect CAGM is yet to be fully investigated.
Green and Romero (2012) and Romero et al (2012) proposed additional empirical gradient methods based on the similar approach to the CAGM in determining ΔTa and finding a linear regression against Vc measured with the T-max method, CHPM or the Marshall-Burgess HRM. The Symmetrical Gradient Method (SGM) extends the Marshall-Burgess HRM into the high velocity range. SGM waits at least 30 seconds after the heat pulse before calculating ΔTa. The result is then regressed against Vc.
The Maximum Derivative Method (MDM, Green and Romero 2012), or the Symmetrical Derivative Method (SDM, Romero et al 2012), finds the maximum rate of change of the ΔTa curve (ΔT’max, i.e. the derivative of ΔTa). The MDM/SDM can be applied to either T-max method, CHPM or Marshall-Burgess HRM.
The accuracy of empirical gradient methods is dependent on the accuracy of Vh or Vc derived from T-max method, CHPM and HRM. Sources of error, such as wounding and probe misalignment, will significantly affect the accuracy of empirical gradient methods. As is the goal with the empirical methods, the measurement range of T-max method, CHPM and HRM has been extended whereby T-max and CHPM can measure to -10 cm/hr and HRM can measure to +70 cm/hr (Green and Romero 2012, Romero et al 2012).
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