heat ratio method sap flow - ict international

13/01/2014 1

Solutions for soil, plant & environmental monitoring

www.ictinternational.com

Heat Ratio Method

&

Sap Flow

ICT International

13/01/2014 2



Definitions

– Stem diameter = stem width

– Xylem = sapwood + heartwood

– Sapwood = conducting tissue

– Heartwood = non-conducting

tissue

13/01/2014 3



Definitions

Positive Flow

Zero Flow

Reverse Flow

Radial Profile

13/01/2014 4



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.

13/01/2014 5




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

13/01/2014 6




13/01/2014 7



Thermistor Location

13/01/2014 8



a c

Temperature sensors

Downstream temperature probe

Upstream temperature

probe

Heater probe x

x

Bark + cambium

Sapwood Heartwood Centre of stem

Sapflow

db

Needles Installed in a Tree

Outer Inner

(a,b) (c,d)

13/01/2014 9



Step 1: Initial Temperature – 31 sec

a c

Temperature sensors



probe

Heater probe x

x

Bark + cambium


Sapflow

db

13/01/2014 10



Step 2: Heater Pulse – 2.68 sec

a c

Temperature sensors



probe

Heater probe x

x

Bark + cambium


Sapflow

db

13/01/2014 11



Step 3: Wait – 60 sec

a c

Temperature sensors



probe

Heater probe x

x

Bark + cambium


Sapflow

db

13/01/2014 12



Step 4: Measure Temp – 40 sec

a c

Temperature sensors



probe

Heater probe x

x

Bark + cambium


Sapflow

db



Raw Temperature Mode – Outer Sensor Tem

pe

ratu

re (

C)

Time (seconds)

0 20 40 60 80 100 120 140

32.4

32.6

32.8

33.0

33.2

33.4

Downstream

Upstream



Time (seconds)

0 20 40 60 80 100 120 140

32.4

32.6

32.8

33.0

33.2

33.4

Step 1: Initial Temperature Tem

pe

ratu

re (

C)

31 seconds initial temperature



Time (seconds)

0 20 40 60 80 100 120 140

32.4

32.6

32.8

33.0

33.2

33.4

Step 2: Heat Pulse Tem

pe

ratu

re (

C) 2.68 seconds

heater pulse



Time (seconds)

0 20 40 60 80 100 120 140

32.4

32.6

32.8

33.0

33.2

33.4

Step 3: 60 second wait Tem

pe

ratu

re (

C)

60 second wait



Time (seconds)

0 20 40 60 80 100 120 140

32.4

32.6

32.8

33.0

33.2

33.4

Step 4: Temperature Measurement Tem

pe

ratu

re (

C)

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

32.4

32.6

32.8

33.0

33.2

33.4

Calculating v1 and v2Tem

pe

ratu

re (

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

v1/v

2

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Heat Pulse


Time (seconds)

20 40 60 80 100 120 140 160

v1/v

2

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Only use the last 40 seconds of data


Time (seconds)

20 40 60 80 100 120 140 160

v1/v

2

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

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

C

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

C

vh = 0.000 cm hr-1

vh =

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

C

vh = -4.523 cm hr-1

vh =

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

C

vh = 0.255 cm hr-1

vh =

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

C

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

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

C

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

Bark



Stem Properties



Total Tree Sap Volume

A1

A2

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

A1

A2

HeartwoodSapwood

Sap flow Sensor



The Radial Profile

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 50 60

Sap

Velo

cit

y(c

mh

r-1)

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

0 5 10 15 20 25 30 35 40 50 60

Sap

Velo

cit

y(c

mh

r-1)

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

0 5 10 15 20 25 30 35 40 50 60

Sap

Velo

cit

y (

cm

hr-

1) Outer Sensor

Inner Sensor

X

X

Large Sapwood – Linear Decrease



0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 50 60

Sap

Velo

cit

y (

cm

hr-

1) Outer Sensor

Inner Sensor

X X

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


[email protected]

Phone: 61 2 6772 6770

Fax: 61 2 6772 7616

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

http://www.ictinternational.com/

mailto:[email protected]

heat ratio method sap flow - ict international

Documents