# Protocol

### Authors

Cleiton B. Eller, Stephen S.O. Burgess, Rafael S. Oliveira

**Overview**

This protocol explains how to set up a sensor to measure sap flow using the heat-ratio method. We also explain how to convert the raw heat-pulse velocity in sap flow data.

**Background**

The Heat-Ratio Method (HRM; Burgess et al. 2001) is a modification of another popular Heat-Pulse Velocity based method to measure sap flow, the Compensation Heat-Pulse Method (CHPM; Swanson and Whitfield 1981, Green and Clothier 1988). The CHPM has been successfully used to measure sap flow in roots and stems in several studies (Becker 1996; Lott et al. 1996; Zotz et al 1997; Burgess et al. 1998). However, CHPM is inaccurate at low sap flow rates (e.g. < 3.6 ± 7.2 cm h^{-1}; Becker 1998) and incapable of measuring reverse sap flow.

The HRM is based on the temperature ratio created between probes positioned symmetrically above and below a line heater. The HRM successfully measures low sap flow rates, being widely used to study sap flow in roots (Burgess et al 1998), nighttime sap flow (Dawson et al 2007; Rosado et al 2012) and during any conditions of low atmospheric demand (Burgess & Dawson 2004). Besides that, the method is capable of accurately measuring reverse-flow, which makes it suitable to study water fluxes resulting from hydraulic redistribution (Burgess et al 1998, Oliveira et al 2005, Burgess and Bleby 2006) and foliar water uptake (Burgess & Dawson 2004, Goldsmith et al 2013; Eller et al 2013). Generally, it is assumed that HRM have a theoretical upper limit to measure sap velocities of 54 cm hr^{-1} (Swanson 1983; Burgess et al 2001). However, laboratory tests using a high-pressure pump and cut stem segments suggests that HRM could measure accurately sap flow ranging from 0-100 cm hr^{-1} (Burgess and Downey 2014). Model simulations from Vandegehuchte et al (2014) also show that HRM provides accurate results even at high sap velocities (up to 100 cm hr^{-1}) when stem temperature gradients are not present.

**Materials/Equipment**

- Thermometer probes, heater probe and data logger (or a commercially available HRM device)
- Drill and drill bits
- Drill guide
- Increment borer
- Bark depth gauge
- Methyl Orange solution (0.1%)
- Measurement tape
- Chisel and mallet

**Units, terms, definitions**

We follow the unifying nomenclature for sap flow measurements given in Edwards et al (1996). The other units and nomenclature follow Burgess et al (2001).

Heat pulse velocity (*v _{h}*, cm hr

^{-1})

Heat pulse velocity corrected for wound effects (*v _{c}*, cm hr

^{-1})

Sap velocity (*v _{s}*, cm hr

^{-1})

Sap flow (*Q*, cm^{3 }hr^{-1})

Temperature increases in downstream and upstream probes after the heat-pulse (*v _{1}* and

*v*, respectively, °C)

_{2}Temperature before and after the heat pulse (*T _{0}* and

*T*, respectively, °C)

_{h}Sapwood thermal diffusivity (*k*, cm^{2} s^{-1})

Fresh sapwood thermal conductivity (*K _{gw}*. J m

^{−1}s

^{-1 }°C

^{ −1})

Dry sapwood matrix thermal conductivity (*K _{w}*, J m

^{–1 }s

^{–1}°C

^{–1})

Fresh sapwood specific heat capacity (*c*, J kg^{–1} °C^{–1})

Dry sapwood specific heat capacity (*c _{w}*, J kg

^{–1}°C

^{–1})

Sapwood density (ρ_{b}, kg m^{-3})

Sapwood specific gravity (*G*, kg_{dry wood} (m^{3}_{wood})^{−1} (kg_{water} (m^{3}_{water})^{−1})^{−1}

Sapwood water content (*m _{c}*, kg)

Sapwood water content at fiber saturation point (*m _{c_FSP}*, kg)

Sapwood void fraction at the fiber saturation point (*F _{v_FSP}*, m

^{3}

_{void }m

^{-3}

_{wood})

Sapwood dry weight (*w _{d}*, kg)

Sapwood fresh weight (*w _{f}*, kg)

Cell wall density (ρ_{cw}, kg m^{-3})

Water thermal conductivity (*K _{s}*, J m

^{–1 }s

^{–1}°C

^{–1})

Water specific heat capacity (*c _{s}*, J kg

^{–1}°C

^{–1})

Water density (ρ_{s}, kg m^{-3})

Wound correction coefficient (*B)*

Total xylem cross-sectional area (CSA, cm^{2})

**Procedure**

The protocol for tree selection and other general sap flow installation recommendations are described **here**. We will discuss only the procedures that are particular to HRM in the sections below.

*Probes positioning*

- In HRM, two thermometer probes are positioned equidistantly from a probe equipped with a heater. In the original HRM principle, the distance between the probes and the heater was 6 mm. Nowadays, the most used distance is 5 mm, as this increases the maximum (theoretical) measurable sap velocity rates from 45 cm hr
^{-1}to 54 cm hr^{-1}(Swanson 1983; Burgess et al 2001). - The thermometers should be positioned on the most active xylem area, which is usually the region closer to the cambium. The recommended distance by Burgess and Downey (2014) is 2.5 mm below the cambium but this might vary among species. An increment borer and a bark depth gauge can be used to assess bark thickness and xylem positioning.
- As sap flow is not constant across the radial sapwood profile (Miller et al 1980; Cohen et al 1981), it is recommended to place more thermometers in each probe to characterize the effect of sapwood depth in sap flow. The commercially available HRM probes have two thermistors in each probe, which allows for the use of the weighted average method (Hatton et al 1990) to integrate the sapflow across the xylem. This procedure is explained in details in the
*Integrating sap flow profile* - When drilling the holes, it is recommended to use a drill guide to assure that the holes are aligned and parallel. The symmetry of the holes can be assessed by inserting drill bits in the holes and inspecting them visually (Burgess and Downey 2014). Small misalignments might still be corrected using the procedure described in details in the
*Calculating Heat-Pulse Velocity*

*Heat-pulse energy and measurement time*

- The HRM is based on the temperature ratio between probes (
*v*); therefore, the absolute temperature of the heat pulse is not important. However, a minimum increase in temperature is necessary to allow the thermometers to register accurately temperature changes. On the other hand, high temperatures might excessively damage the tissues around the needle, thermally decoupling it from the sapwood and compromising the accuracy of the measurements. Burgess and Downey (2014) recommend keeping the maximum temperature rise after the heat-pulse in a range between 0.7° and 1.5° C._{1}/v_{2} - The changes in the
*v*should become approximately linear 60 s after the heat-pulse. Therefore, thermometer measurements should be conducted between 60 to 100 s after the heat-pulse. Multiple_{1}/v_{2}*v1/v2*sampling is recommended to minimize random variation caused by thermal or electronic interference (Burgess et al 2001).

*Calculating heat-pulse velocity*

In HRM, the heat-pulse velocity (*V _{h}*; cm hr

^{-1}) is calculated using the Marshal’s (1958) equation:

V_h= k/x ln(v_1/v_2 )3600 (1)

where *k *is the thermal diffusivity of fresh wood, x is the distance (in cm) between the heater and the probes, and *v _{1}* and

*v*are the downstream and upstream temperature increases after the heat-pulse, that is:

_{2}

v=T_h- T_0 (2)

where *T _{h}* is the probe temperature after the heat pulse and

*T*the probe temperature before the heat pulse.

_{0}

*Calculating thermal diffusivity*

In the original HRM protocol, *k *is initially set to a nominal value of 2.5 × 10^{–3} cm^{2} s^{–1} (Marshal 1958). Afterwards, Burgess et al (2001) proposed two independent methods to estimate actual *k*: simultaneously using CHPM and HRM to resolve for *k *(as CHPM does not require *k *it is possible to solve HRM and CHPM equations simultaneously)*. *The results from this approach were similar to an analytical approach employed by Burgess et al (2001). In this approach, *k *is estimated using Marshall’s (1958) equation:

k=K_gw/(ρ_b c) 10000 (3)

where *K _{gw }*is the green (fresh) sapwood thermal conductivity, ρ

_{b}is sapwood density (kg m

^{-3}; which can be calculated using this

**protocol**) and

*c*the specific heat capacity of fresh sapwood. The value of

*K*can be calculated using a modified Swanson (1983) equation:

_{gw }

K_gw= K_s m_c ρ_b/ρ_s +K_w (1-m_c ρ_b/ρ_s ) (4)

where *K _{s}* is the water thermal conductivity (5.984 × 10

^{–1}J m

^{–1 }s

^{–1}°C

^{–1}at 20 °C),

*m*is the sapwood water content (kg) and ρ

_{c}_{s }is the density of water (999.97 kg m

^{-3}).

*K*is thermal conductivity of the dry wood matrix, calculated following Swanson (1983):

_{w}

K_w=0.04182 (21-20(1-((ρ_b 0.6536+m_c)/1000))) (5)

the value of *c *is estimated using a modified Edwards and Warwick (1984) equation:

c= (((w_d c_w + c_s ) (w_f-w_d))/w_f ) (6)

where *c _{w}* is the specific heat of the wood matrix (1200 J kg

^{-1}°C

^{-1}at 20°C),

*w*is sapwood fresh weight and

_{f}*w*is sapwood dry weight (kg).

_{d}Despite this approach producing results that agree well with the simultaneous solution and with the gravimetric validation experiments conducted by Burgess et al (2001), Vandegehuchte and Steppe (2012) suggest that the approach used by Burgess et al (2001) to calculate *K _{gw} *might produce errors of up to 10% in sap velocity estimates. According to Vandegehuchte and Steppe (2012) the mixture model used by Burgess can only be applied in sapwood with

*m*lower than its fiber saturation point (

_{c}*i.e.*the point where only bound water is present in the sapwood). As living, transpiring trees have a sapwood

*m*higher than its fiber saturation point, Vandegehuchte and Steppe (2012) suggest the use of the following equation:

_{c}

K_gw= K_w (m_c- *m _{c_FSP}* ) ) ρ_b/ρ_s +0.04186 (21-20

*F*

_{v_FSP}) (7)

where *m _{c_FSP }*is the sapwood water content at fiber saturation point and

*F*

_{v_FSP }is the void fraction at the fiber saturation point. The value of

*m*can be determined following Roderick and Berry (2001):

_{c_FSP }

*m _{c_FSP}* = 0.2 (ρ_b ρ_s

^{-1})

^{-1/2}(8)

while *F*_{v_FSP }is can be estimated with the following equation:

*F*_{v_FSP}=1 - G ((ρ_s/*ρ _{cw} *)+

*m*) (9)

_{c_FSP}

where *G* is sapwood specific gravity (ρ_{b}/ρ_{s}), and ρ_{cw }is cell wall density (1530 kg m^{−3}, Kollmann and Côté (1968)).

*Correction for probe misalignment*

Probe misalignment in HRM is measured *in situ*, taking into account any thermal and physical asymmetries. In order to correct misalignment, *V _{h }*= 0 must be imposed. The most reliable way to impose

*V*= 0 is to sever the stem or root with the probes to stop sap flow (Burgess et al 2001, Burgess & Dawson 2004, Oliveira et al 2005). Care must be taken to avoid moving the probes during the severing process; otherwise the correction would be made for the new sensor position and would be invalid. Some authors (Goldsmith et al 2013, Rosado et al 2012) assume that

_{h }*V*during certain environmental conditions (usually very humid nights) approximates to zero, and use the data from these periods in the correction.

_{h}At *V _{h }*= 0, probe spacing is calculated as:

x_2= √(4kt ln(v_1/v_2 )+x_1^2 ) (10)

where *x _{2 }*is the incorrectly placed probe,

*x*is assumed to be correctly placed probe (at

_{1}*x*cm from the heater) and

*t*is the measurement time (i.e. the time interval in seconds after the heat pulse is emitted when the thermometer probes register the temperatures). Once

*x*and

_{1}*x*are estimated, corrected

_{2}*V*is calculated as:

_{h }

V_h= (4kt ln(v_1/v_2 )-(x_2^2 )+(x_1^2))/(2t(x_1-x_2)) 3600 (11)

As it is usually unknown which probe is incorrectly positioned, it is recommended to solve equations 9 and 10 for *x _{1}* and

*x*, and average both solutions. This correction can be made only for a subset of the sap flow data. The corrected values should be linearly correlated with the uncorrected values; therefore, it is possible use the equation derived from a least-squares linear regression between corrected and uncorrected values to correct the remaining data (Burgess et al 2001).

_{2}* *

*Correction for wounding*

The HRM probes can cause substantial mechanical damage in the wood. The probes interrupt the flow pathway where they were inserted, and the region surrounding the probes might become occluded by tylose formation (Barret et al 1995). This non-conducting wood area causes departure of the measured *V _{h}*. from actual

*V*. This departure follows an approximately linear function; therefore, the wound corrected

_{h}*V*(

_{h}*V*) can be obtained simply by multiplying

_{c}*V*by a correction coefficient (

_{h}*B*) based on wound width (Burgess et al 2001):

V_c=V_h B (12)

wound width can be determined by following this **protocol**. The *B* for commonly found wound widths for 0.5 mm probe configurations is given in the table below (reproduced from Burgess et al 2001):

Wound width (cm) | Correction coefficient (B) |

0.17 | 1.7283 |

0.18 | 1.7853 |

0.19 | 1.8568 |

0.20 | 1.9216 |

0.21 | 1.9891 |

0.22 | 2.0594 |

0.23 | 2.1326 |

0.24 | 2.1825 |

0.26 | 2.3176 |

0.28 | 2.4813 |

0.30 | 2.6383 |

* *

*Correction for stem temperature variation*

Recently, Vandegehuchte et al (2014) have demonstrated that temporal variations in stem temperature might create errors of up to 40% in HRM *V _{h}*. These errors are attributed to the time interval (60-100 s) between the heat-pulse and the thermometer measurements. Vandegehuchte et al (2014) propose a simple solution to these errors by including a temperature correction in the data obtained by HRM.

To do that, Vandegehuchte et al (2014) determined the slope and intercept of the stem temperature variations over a 30 s period before the heat-pulse. The projected values of temperature were subtracted from the measured temperature values during and after the heat-pulse application. Therefore, *v *in equation 2 would become:

v =(T_h - ̂ T_h)-(T_0 - ̂ T_0 ) (13)

*Calculating sap velocity*

The *V _{c }*is composed by the weighted average of the velocity of moving sap and the stationary wood in the xylem (Marshall 1958). Therefore, we can relate

*V*to actual sap velocity (

_{c}*V*) by measuring the fractions of sap and wood in the xylem (basically, the sapwood water content), and accounting for their different densities and specific heat. Burgess et al (2001) uses a modified Marshall’s (1958) equation to calculate

_{s}*V*(cm hr

_{s }^{-1}):

V_s= (V_c ρ_b (c_w+m_c c_s))/(ρ_s c_s ) (14)

where *c _{s}* is water specific heat (4182 J Kg

^{-1}°C

^{-1}at 20°C).

*Calculating sap flow*

Sap flow (*Q; *cm^{3} hr^{-1}) is easily derived from *V _{s }*by multiplying it by the total xylem cross-sectional area (CSA; cm

^{2}):

Q=V_s CSA (15)

estimating CSA can be done by following one of the methods described **here**. Alternatively, when it is hard to differentiate between active and inactive xylem, it is possible to use the method used by Goldstein et al (1998). In this method, dye is injected in holes made with an increment borer (other authors prefer to use drills or a chisel and mallet) at the base of the tree. After some time (1-2 h), a sample is collected with an increment borer 2-4 cm above the point where the dye was injected. The area of conducting tissue is determined by the extension of the sapwood colored by the dye.

*Integrating sap flow depth profile*

Assuming that sap flow is uniform along the sapwood depth profile might produce large errors (-90 to 300%; Nadezhdina et al 2002). One common and robust method for integrating sap flow depth profile is to use the weighted average method (Hatton 1990). In this method, if a set of *n *sensors are placed at different depths between the cambium and the heartwood, the tree total CSA is divided into *n *concentric annuli. The inner radius (*r _{k}*) of a given annulus

*k*, occurs midway between sensors

*k*and

*k*+1, where

*k*= 1 ,…,

*n*-1. This way, all points within the annulus

*k*are closer to the sensor

*k*than any other sensor; then we assume that

*V*captured by sensor

_{s}*k*(

*V*) represents the entire annulus

_{sk}*k*. Following this logic, the total sap flow of a tree being monitored by

*n*sensors is the sum of the sap flow of its

*n*concentric annuli:

Q= ∑_k^n* _{=1 }*π (r_k^2-r_k^2

*)V*

_{-1}*(16)*

_{sk}

Hatton (1990) recommends keeping the area of each annuli constant, so every sensor contributes with an equal amount of information to *Q *profile. Therefore, the spacing between sensors should decrease, as they get closer to the cambium. More details on how to space the sensors to achieve this can be found on Hatton (1990).

**Links to resources and suppliers**

**Literature references**

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