a brief introduction to the dual method approach (DMA)

Author: Michael A. Forster

Edaphic Scientific Pty Ltd

School of Agriculture and Food Science, The University of Queensland

The Dual Method Approach (DMA) is a measurement of sap flow that can resolve fast, slow, zero and reverse rates of flow. The DMA is based on the heat pulse velocity (HPV) family of measurement techniques, combining two well-known equations into a single approach. The DMA unites Marshall’s (1958) Slow Rates of Flow Method (SRFM) with Cohen et al’s (1981) T-Max method in a single measurement. The DMA improves the SRFM and T-Max methods by expanding the measurement range of heat pulse velocity, while minimising sensing and data logging requirements. The DMA is, therefore, a more accurate and cost-effective technique of sap flow measurements.

the problem with existing heat pulse velocity techniques

The main problem with existing heat pulse velocity techniques is their inability to resolve the complete range of heat velocity observed in plants. The various methods within the heat pulse family of techniques can only resolve a partial range of heat velocity. The Dual Method Approach overcomes this limitation as it measures the full range from reverse, zero to extremely high rates of heat velocity.

The SRFM was initially proposed by Marshall in the appendix of his ground breaking 1958 publication on heat pulse velocity techniques for sap flow measurements. As the SRFM name implies, it is a method to use when “it is desired to distinguish accurately between rather slow rates of flow (V [heat velocity] less than 10 or 15 cm/hr) and definitely zero flow” (Marshall, 1958, p: 395). Subsequent research found that the SRFM cannot resolve rates of velocity >~40 cm/hr (Bleby et al 2008; Pearsall et al 2014).

The T-Max method was proposed by Cohen et al (1981) as an improvement on heat pulse velocity techniques outlined by Marshall (1958). Subsequent testing of the accuracy of the T-Max method showed that it is highly accurate at fast flows, but poor at slow and zero flows (Green et al 2009). Due to the sensor design, the T-Max method cannot measure reverse sap flow. The ideal measurement heat velocity range for T-Max is ~10 cm/hr to > 200 cm/hr.

how does the DMA work?

The DMA is an algorithmic technique that extracts the most accurate data measurements from the SRFM and T-Max methods to output a single heat velocity value. During periods of slow, zero or reverse velocity, the DMA extracts data from the SRFM; during periods of moderate to fast velocity, the DMA extracts data from the T-Max. The output value is heat velocity which, when combined with known parameters for wound correction and wood properties, can be used to subsequently estimate sap velocity, sap flow and whole plant water use.

The DMA can legitimately combine data from the SRFM and T-Max methods as these are derivative equations from the conduction/convection equation of heat transport in materials (Marshall 1958). Numerous studies have demonstrated that two heat pulse velocity techniques, derived from the conduction/convection equation, output similar heat velocities with a linear regression slope of 1 (González-Altozano et al 1998, 2008; Jones et al 1988; Pearsall et al 2014; Romero et al 2012; Vandegehuchte and Steppe 2012). Therefore, switching between different methods, where one method is weak and the other strong, is valid.

Previous studies have combined heat pulse velocity techniques with success. For example, Cohen et al (1988, 1993) combined the T-Max and Compensation Heat Pulse Method (CHPM) for measuring slow to very fast rates of flow, and Pearsall et al (2014) combined the CHPM and SRFM to measure reverse, zero, slow and fast rates of flow in grapevines. However, combining T-Max with CHPM cannot resolve zero or reverse rates of sap flow; and combining the CHPM with the SRFM requires significant sensing and data logging capacity which limits its practicality. The Dual Method Approach resolves zero and reverse flows, and it minimizes the amount of sensing and data logging requirements, which improves its practical use.

probe and sensor configuration

Edaphic Scientific supplies the HPV-06 Sap Flow Sensor which is configured for the DMA. Edaphic Scientific also supplies the data acquisition systems required to support the HPV-06 Sap Flow Sensor.

The DMA requires three probes, two temperature and one heater probe, spaced at equal distances. The top (downstream) and bottom (upstream) are the temperature probes, and the middle probe is the heater:

DMA Sap Flow Sensor

an example data set

The following example data were derived from an installation on a Merlot grapevine (Vitis vinifera ‘Merlot’) growing in New South Wales, Australia, during a summer period. The grapevine was well irrigated and fertilised and growing under ideal viticultural conditions. A six-day period of the entire measurement campaign was extracted for demonstration purposes. The period covers days of sunny/hot and cloudy/cooler weather. The following data is heat velocity uncorrected for wounding and with thermal diffusivity (k) independently quantified by a thermal diffusivity meter (TEMPOS, METER Group) during a period of zero sap flow.

Over this measurement period, the data derived from the SRFM showed a maximum daytime value of 18.9 cm/hr and a minimum night-time value of 0.2 cm/hr:

SRFM Sap Flow Data

In contrast, data derived from the T-Max showed a maximum daytime value of values of 89.1 cm/hr and a minimum night-time value of 9.8 cm/hr:

Tmax Sap Flow Data

When the data are presented in the same figure, the measurement range limitations of respective methods are clearly highlighted:

Sap Flow Data Example

The DMA algorithm states that when heat velocity is < 15 cm/hr, use data from SRFM; and when heat velocity > 15 cm/hr, use data from T-Max. The following figure is the result when the DMA algorithm is applied to the above data:

Dual Method Approach Sap Flow Data


The Dual Method Approach is an improvement on previous heat pulse velocity techniques as it measures the entire range of heat velocity in plants. The DMA minimizes the number of probes that need to be installed into stems and is a practical method for sap flow measurements.


Bleby et al. 2008. Limitations of the HRM: great at low flow rates, but no yet up to speed? In ‘7th International Workshop on Sap Flow: Book of Abstracts’. (International Society of Horticultural Sciences: Seville, Spain).

Cohen et al. 1981. Improvement of the heat pulse method for determining sap flow in trees. Plant Cell Environ., 4, 391–397.

Cohen et al. 1988. Calibrated Heat Pulse Method for Determining Water Uptake in Cotton. Agron. J., 80, 398-402.

Cohen et al. 1993. Accuracy of Sap Flow Measurement Using Heat Balance and Heat Pulse Methods. Agron. J., 85, 1080-1086.

González-Altozano et al. 1998. Sap flow determination in citrus trees by heat pulse techniques. 4th International Workshop on Measuring Sap Flow in Intact Plants, Brno, Czech Republic.

González-Altozano et al. 2008. Comparative assessment of five methods of determining sap flow in peach trees. Agricul. Water Manag. 95, 503-515.

Green et al. 2009. A re-analysis of heat pulse theory across a wide range of sap flows. Acta Hort., 846, 95–104.

Jones et al. 1988. Evaluation of various heat-pulse methods for estimation of sap flow in orchard trees: Comparison with micrometeorological estimates of evaporation. Trees, 2, 250–260.

Marshall. 1958. Measurement of sap flow in conifers by heat transport. Plant Physiol., 33, 385–396.

Pearsall et al. 2014. Evaluating the potential of a novel dual heat-pulse sensor to measure volumetric water use in grapevines under a range of flow conditions. Funct. Plant Biol., 41, 874–883.

Romero et al. 2012. Improving Heat-Pulse Methods to Extend the Measurement Range Including Reverse Flows. Proceedings of the VIIIth International Workshop on Sap Flow. Acta Hort, 951, 31-38.

Vandegehuchte and Steppe. 2012. Sapflow+: a four-needle heat-pulse sap flow sensor enabling nonempirical sap flux density and water content measurements. New Phytologist, 196, 306-317.