Heat Ratio Method Sap Flow - ICT International

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Solutions for soil, plant & environmental monitoring

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Heat Ratio Method

Sap Flow

ICT International

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Definitions

– Stem diameter = stem width

– Xylem = sapwood + heartwood

– Sapwood = conducting tissue

– Heartwood = non-conducting

tissue

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Definitions

Positive Flow

Zero Flow

Reverse Flow

Radial Profile

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A Brief History of HRM…

– 1998 to 2000, limitations with

existing methods

– Low and reverse flow

– Dr Stephen Burgess,

University of Western Australia

– Seminal publication:

Burgess et al. (2001) Tree Physiology 21: 589-598.

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Burgess et al. (2000) Annals of Botany 85: 215-224

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Thermistor Location

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Temperature sensors

Downstream temperature probe

Upstream temperature

Heater probe x

Bark + cambium

Sapwood Heartwood Centre of stem

Sapflow

Needles Installed in a Tree

Outer Inner

(a,b) (c,d)

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Step 1: Initial Temperature – 31 sec

Temperature sensors

Heater probe x

Bark + cambium

Sapflow

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Step 2: Heater Pulse – 2.68 sec

Temperature sensors

Heater probe x

Bark + cambium

Sapflow

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Step 3: Wait – 60 sec

Temperature sensors

Heater probe x

Bark + cambium

Sapflow

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Step 4: Measure Temp – 40 sec

Temperature sensors

Heater probe x

Bark + cambium

Sapflow

Raw Temperature Mode – Outer Sensor Tem

Time (seconds)

0 20 40 60 80 100 120 140

Downstream

Upstream

Time (seconds)

0 20 40 60 80 100 120 140

Step 1: Initial Temperature Tem

31 seconds initial temperature

Time (seconds)

0 20 40 60 80 100 120 140

Step 2: Heat Pulse Tem

C) 2.68 seconds

heater pulse

Time (seconds)

0 20 40 60 80 100 120 140

Step 3: 60 second wait Tem

60 second wait

Time (seconds)

0 20 40 60 80 100 120 140

Step 4: Temperature Measurement Tem

40 second measurement period

vh = heat velocity k = thermal diffusivity v1 = average increase temperature downstream v2 = average increase temperature upstream x = distance of temperature needles from heater needle 3600 = converting from seconds to hours

Raw Heat Velocity Equation

Time (seconds)

0 20 40 60 80 100 120 140

Calculating v1 and v2Tem

C) v1 = 0.538 C

v2 = 0.294 C

on oil, & en

Calculating v1 and v2

Time (seconds)

20 40 60 80 100 120 140 160

Heat Pulse

Time (seconds)

20 40 60 80 100 120 140 160

Only use the last 40 seconds of data

Time (seconds)

20 40 60 80 100 120 140 160

Linear Equation for last 40 seconds of data:

y = 0.0004x + 1.82

Note slope is less than 0.01

Raw Heat Velocity Equation

k = 0.0025 cm2 s-1

x = 0.5 cm v1 = 0.538 C v2 = 0.294

vh = 10.865 cm hr-1

ZERO Flow:

k = 0.0025 cm2 s-1

x = 0.5 cm v1 = 1.0 C v2 = 1.0

vh = 0.000 cm hr-1

Raw Heat Velocity Equation – Zero Flow

REVERSE Flow:

k = 0.0025 cm2 s-1

x = 0.5 cm v1 = 0.7 C v2 = 0.9

vh = -4.523 cm hr-1

Raw Heat Velocity Equation – Reverse Flow

LOW Flow:

k = 0.0025 cm2 s-1

x = 0.5 cm v1 = 0.71 C v2 = 0.70

vh = 0.255 cm hr-1

The logarithm of v1/v2 allows for low flow

Raw Heat Velocity Equation – Low Flow

vh = heat velocity k = thermal diffusivity v1 = average increase temperature downstream v2 = average increase temperature upstream x = distance of temperature needles from heater needle 3600 = converting from seconds to hours

Raw Heat Velocity & Thermal Diffusivity

Thermal Diffusivity

Definition:

The thermal conductivity of a substance divided by the product of its density and its

specific heat capacity.

Marshall (1958): k = 0.0025 cm2 s-1

Values range between 0.0014 (water) and

0.004 (dry wood)

Measure directly with Decagon’s KD2 Pro:

Thermal Diffusivity – Empirical Technique

Equation 8:

k = thermal diffusivity Kgw = thermal conductivity p = basic density of wood (dry weight/fresh volume) c = specific heat capacity of fresh wood matrix

Equation 9:

Ks = thermal conductivity of water (5.984 x 10-1 J m-1 s-1 at 20 C) Kw = thermal conductivity of dry wood matrix (see next slide) pb = basic density of wood (dry weight/fresh volume) cw = specific heat capacity of wood matrix cs = specific heat capacity of sap mc = water content of sapwood ps = density of water

cw = 1200 J kg-1 C-1 at 20 C cs = 4182 J kg-1

C-1 at 20

ps = 998.2071 kg m-3 at 20 C

Equation 9:

pb = basic density of wood (dry weight/fresh volume)

mc = water content of sapwood

Equation 9:

– Collect sapwood sample

– Fresh weight as soon as possible

– Volume: cylinder or Archimedesprinciple

– Dry weight: 2 days in oven at 60°C

Fresh & Dry Weight, and Fresh Volume

Equation 10:

Equation 11:

Equation 9:

Fv = void fraction

Equation 12:

wf = fresh weight (kg) wd = oven dried weight (kg)

Equation 8:

Converting Raw Data to Sap Flow

Heat Velocity

Wound Response & Wood Properties: Fresh and dry weight, fresh volume

Sap Velocity

Stem Properties: Bark, sapwood, heartwood, diameter

Sap Flow

Wound Response

Table 1:

Equation 6:

Calculating Sap Velocity

Equation 7:

Vs = sap velocity Vc = heat velocity corrected for wound diameter pb = basic density of wood (dry weight/fresh volume) cw = specific heat capacity of wood matrix cs = specific heat capacity of sap mc = water content of sapwood ps = density of water

Equation 7:

cw = 1200 J kg-1 C-1 at 20 C cs = 4182 J kg-1

C-1 at 20

ps = 998.2071 kg m-3 at 20 C

Equation 7:

pb = basic density of wood (dry weight/fresh volume)

mc = water content of sapwood

– Collect sapwood sample

– Fresh weight as soon as possible

– Volume: cylinder or Archimedesprinciple

– Dry weight: 2 days in oven at 60°C

The Heat Ratio Method

Heat Velocity

Wound Effect, Thermal Diffusivity & Wood Properties: Fresh and dry weight, fresh volume

Sap Velocity

Stem Properties: Bark, sapwood, heartwood, diameter

Sap Flow

Calculating Sap Flow

Sapwood

Heartwood

Stem Properties

Total Tree Sap Volume

Heartwood Sapwood

A1 = Sapwood Annulus 1

A1 = Outer Sensor

A2 = Sapwood Annulus 2

A2 = Inner Sensor

Sap flow Sensor

Total Tree Sap Volume

A1 = 2.4 units

A2 = 1.1 unit

Sap Volume = 3.5 units

HeartwoodSapwood

Sap flow Sensor

The Radial Profile

0 5 10 15 20 25 30 35 40 50 60

Radial Distance from Outside of Stem (mm)

Note: demonstration data only

Bark Heartwood

The Radial Profile – Heat Ratio

Method

0 5 10 15 20 25 30 35 40 50 60

Radial Distance from Outside of Stem (mm)

Note: demonstration data only

Bark Heartwood

Outer Sensor

Inner Sensor

Total Tree Sap Volume – Large Sapwood

0 5 10 15 20 25 30 35 40 50 60

1) Outer Sensor

Inner Sensor

Large Sapwood – Linear Decrease

0 5 10 15 20 25 30 35 40 50 60

1) Outer Sensor

Inner Sensor

Large Sapwood – Hold Value

Tree Water Use Californian Redwood, over 100m tall

Approx. 2000 litres per day

Coolibah, 18m tall Approx. 260 litres per day

Wattle, 4m tall Approx. 15 litres per day

Eucalypt Sapling, 1.5m tall Approx. 0.2 litres per day

ICT International Pty Ltd Solutions for soil, plant and environmental monitoring

Sales@international.com

Phone: 61 2 6772 6770

Fax: 61 2 6772 7616

PO Box 503, Armidale, NSW, Australia, 2350 INTERNATIONAL

Heat Ratio Method Sap Flow - ICT International

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