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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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A Brief History of HRM…
Burgess et al. (2000) Annals of Botany 85: 215-224
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A Brief History of HRM…
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Thermistor Location
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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)
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Step 1: Initial Temperature – 31 sec
a c
Temperature sensors
Downstream temperature probe
Upstream temperature
probe
Heater probe x
x
Bark + cambium
Sapwood Heartwood Centre of stem
Sapflow
db
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Step 2: Heater Pulse – 2.68 sec
a c
Temperature sensors
Downstream temperature probe
Upstream temperature
probe
Heater probe x
x
Bark + cambium
Sapwood Heartwood Centre of stem
Sapflow
db
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Step 3: Wait – 60 sec
a c
Temperature sensors
Downstream temperature probe
Upstream temperature
probe
Heater probe x
x
Bark + cambium
Sapwood Heartwood Centre of stem
Sapflow
db
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Step 4: Measure Temp – 40 sec
a c
Temperature sensors
Downstream temperature probe
Upstream temperature
probe
Heater probe x
x
Bark + cambium
Sapwood Heartwood Centre of stem
Sapflow
db
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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
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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
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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
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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
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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
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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
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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
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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
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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
Only use the last 40 seconds of data
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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
Linear Equation for last 40 seconds of data:
y = 0.0004x + 1.82
Note slope is less than 0.01
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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
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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
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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
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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
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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
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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:
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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
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Thermal Diffusivity – Empirical Technique
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
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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:
Thermal Diffusivity – Empirical Technique
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pb = basic density of wood (dry weight/fresh volume)
mc = water content of sapwood
Thermal Diffusivity – Empirical Technique
Equation 9:
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– 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
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Thermal Diffusivity – Empirical Technique
Equation 10:
Equation 11:
Equation 9:
Fv = void fraction
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Thermal Diffusivity – Empirical Technique
Equation 12:
wf = fresh weight (kg) wd = oven dried weight (kg)
Equation 8:
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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
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Wound Response
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Wound Response
Table 1:
Equation 6:
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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
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Calculating Sap Velocity
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
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Calculating Sap Velocity
Equation 7:
pb = basic density of wood (dry weight/fresh volume)
mc = water content of sapwood
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Calculating Sap Velocity
– Collect sapwood sample
– Fresh weight as soon as possible
– Volume: cylinder or Archimedesprinciple
– Dry weight: 2 days in oven at 60°C
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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
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Calculating Sap Flow
Sapwood
Heartwood
Bark
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Stem Properties
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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
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Total Tree Sap Volume
A1 = 2.4 units
A2 = 1.1 unit
Sap Volume = 3.5 units
A1
A2
HeartwoodSapwood
Sap flow Sensor
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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
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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
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Total Tree Sap Volume – Large Sapwood
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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
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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
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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
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ICT International Pty Ltd Solutions for soil, plant and environmental monitoring
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Phone: 61 2 6772 6770
Fax: 61 2 6772 7616
PO Box 503, Armidale, NSW, Australia, 2350 INTERNATIONAL