# a static approach to measuring a dynamic process

Most researchers are careful with their collection of data. Yet, there is still one significant source of error that is seldom explicitly addressed in any peer-review paper. That source of error is sapwood moisture content.

The parameters that contribute to a sap flow measurement are dynamic and change daily, weekly and seasonally with plant physiology and environment. Just about all researchers treat the parameters as static by only measuring them once either at the start or end of a measurement campaign.

For heat pulse velocity sap flow methods, this problem is particularly acute with a static measurement of sapwood moisture content, also known as stem water content. This parameter is highly variable and changes on a diurnal cycle as well as under different environmental, irrigation or experimental treatments. Yet, in virtually all published papers using heat pulse velocity to estimate sap flow, sapwood moisture content is only measured once.

Fortunately, the HPV-06 Heat Pulse Velocity Sensor from Implexx Sense can simultaneously measure sap flow and stem water content. The HPV-06 provides a solution to dynamically measure sap flow parameters to improve the accuracy of sap flow measurements. This article explains how sapwood water content is dynamic but treated as a static parameter as well as offering a solution to this problem.

##### what is a static equation?

The following is the equation for sap flux density (SFD; cm3/cm2/hr):

where Vc is heat velocity, pd and pw are the basic density (kg m-3) of dry wood and water, respectively, cd and cw are the specific heat capacity of dry wood matrix and sap solution, respectively, and mc is sapwood water content (kg/kg).

The parameter Vc is obviously a variable as this is measured with a sap flow sensor such as the HPV-06 Heat Pulse Velocity Sensor.

The parameters pd and pw are constants. The pd value is found by dividing sapwood dry weight by fresh volume, and pw is a constant with value of 1000.

The parameters cd and cw, on the other hand, offer the first signs of trouble. The cd and cw are assumed to be constants with assigned values of 1200 and 4182 (J/kg/°C), respectively. However, the values of 1200 and 4182 are valid only at 20°C. Becker and Edwards (1999) provide a table outlining how cd and cw vary with temperature. Fortunately, cw does not vary greatly from a value of 4182. Unfortunately, cd does vary between 1100 and 1350 as temperature varies between 0 and 50°C. Most sap flow researchers would consider such variability inconsequential and use the default values of 1200 and 4182.

The critical parameter, however, in the SFD equation is mc. It is well known that sapwood moisture content, or stem water content, is variable throughout the day as well as across seasons and environmental conditions. For example, Constantz and Murphy (1990) measured a change in sapwood water content of 67% in Aesculus californica. However, just about all sap flow calculations measure mc once, either at the start or end of a measurement campaign, and it is extremely rare for a study to continuously measure mc. In the SFD equation, parameters that are variable are treated as constant. This is what makes analysis of sap flow data as static rather than dynamic. That the SFD equation is treated as static has unknown consequences for the accuracy of sap flow measurements primarily because this has never been systematically studied. Other studies, nonetheless, suggest that it is a significant problem.

##### the importance of stem water content for heat pulse velocity sensors

A study by Steppe et al (2010) examined the accuracy of three different types of sap flow methods. All three methods were found to underestimate true sap flow between 35% and 60%. Steppe et al conducted an error analysis of each parameter within each method to determine which parameter was mostly contributing to the underestimation of sap flow. Although the errors varied for each method, for the heat pulse method it was found that mc (specifically, the sapwood fresh weight) was the most significant parameter causing error.

In another study, Lopez-Bernal et al (2014) used desorption curves to demonstrate that changes in mc can lead to significant errors in thermal diffusivity and sap flux density calculations. Lopez-Bernal et al concluded that “ignoring seasonal and daily variations in [mc] might result in large errors in calculated sap flux”.

##### how to be more dynamic with your sap flow measurements

The HPV-06 sensor from Implexx Sense provides a solution to simultaneously measure heat velocity, sap flux density and stem water content. Numerous parameters can be derived from the HPV-06 sensor which can subsequently be used in the thermal conductance and convection equations originally proposed by Marshall (1958). A data table, derived from HPV-06 measurements, can output variables such as heat velocity, maximum temperatures, specific heat capacity, and other variables which can be used in the dynamic calculation of sap flux density and stem water content. For more details, contact Edaphic Scientific who can assist you with your data collection.

##### references

Becker, P.; Edwards, W.R.N. Corrected heat capacity of wood for sap flow calculations. Tree Physiology 1999, 19, 767-768.

Constantz, J. and F. Murphy. 1990. Monitoring moisture storage in trees using time domain reflectometry. J. Hydrology 1990, 119:31–42.

López-Bernal, Á.; Alcántara, E.; Villalobos, F.J. Thermal properties of sapwood fruit trees as affected by anatomy and water potential: errors in sap flux density measurements based on heat pulse methods. Trees 2014, 28, 1623–1634.

Marshall, D.C. Measurement of sap flow in conifers by heat transport. Plant Physiology1958, 33, 385–396.

Steppe, K.; De Pauw, D.J.W.; Doody, T.M.; Teskey, R.O. A comparison of sap flux density using thermal dissipation, heat pulse velocity and heat field deformation methods. Agricultural and Forest Meteorology 2010, 150, 1046–1056.