sap flow data analysis presentation - ict international
TRANSCRIPT
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Sap Flow
Data Analysis
&
Presentation:
How to analyze sap flow data
Michael Forster
ICT International
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Tem
pera
ture
(°C
)
0
10
20
30
40
Rela
tive H
um
idity
(%)
20
40
60
80
100
E. cladocalyx
Time vs Relative Humidity
VP
D (
kP
a)
0
1
2
3
4
5
Rain
fall
(mm
)
0
20
40
60
80
100
J (
cm
3 c
m-2
day
-1)
0
20
40
60
80
100
J (
cm
3 c
m-2
day
-1)
0
20
40
60
80
100
2009 2010 2011
Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar
J (
cm
3 c
m-2
day
-1)
0
20
40
60
80
100
(A)
(B)
(C)
(D) – E. cladocalyx
(E) – E. melliodora
(F) – E. polybractea
Summary Data
• Method:
• Collate entire data sets
• Daily averages or some other summary stat
• Typical variables:
• Temperature
• Relative Humidity
• VPD
• Solar Radiation
• Rainfall
• Wind Speed
• Soil Moisture
• Sap Flow
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Summary Data
Source: Fig 1. Ambrose et al.,2010
• Interpreting Data:
• Visual summary only
• Gives the reader an quick and
easy overview of conditions
during the study
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Representative Data
Source: Figs 3 and 4. Ambrose et al.,2010
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Summary Tables: Tree Characteristics
Source: Table 1. Ambrose et al.,2010 Source: Table 1. Pfautsch & Adams 2012
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Summary Tables: Descriptive Statistics
Source: Table 2. Ambrose et al.,2010
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Summary Tables: Descriptive Statistics
Species Summer ‘10 Autumn ‘10 Winter ‘10 Spring ‘10 Summer ‘11
E. cladocalyx 26.35 (±8.49) 17.02 (±6.59) 11.21 (±4.29) 17.25 (±4.33) 26.59 (±4.18)
E. melliodora 4.63 (±2.53) 2.67 (±1.43) 2.12 (±1.56) 4.59 (±2.52) 9.21 (±4.60)
E. polybractea 7.46 (±7.82) 4.76 (±5.01) 3.62 (±3.52) 8.16 (±7.57) 4.97 (±1.36)
Table 1. Summary of average daily water use (Q, L day-1) throughout the various seasons of the study period.
Values are total tree water use including multiple stems of E. melliodora and E. polybractea. Values are litres of
water (
SD).
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Time
Jan Feb Mar Apr
Cum
ula
tive
Q (
L d
ay-1
)
0
500
1000
1500
2000
2500
Summary Figures: Total or Cumulative
Amounts
Source: Fig. 1. Doronila & Forster in press.
E. cladocalyx
E. melliodora
E. polybractea
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Summary Figures: Total or Cumulative
Amounts
Ambient Elevated Ambient Elevated
Wet Soils Dry Soils
• Statistical Test:
• ANOVA with a Tukey’s
HSD post-hoc test
Source: Fig. 4. Zeppel et al. 2011
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Summary Figures: Treatment Effects
Source: Fig. 4. Ghuran et al., 2013 Source: Fig. 2. Pfautsch & Adams 2012
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Summary Figures: Treatment Effects
1:1 Relationship
Measured
Relationship
Source: Unpublished, R. Duursma,
University of Western Sydney
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Summary Figures: Treatment Effects
• E = Elevated CO2 Treatment
• A = Ambient CO2 Treatment:
• Horizontal line = 1:1 Relationship
• Interpretation:
• Day-time: Trees growing under ambient
CO2 have higher sap flow in both wet
and dry soils
• Night-time: Trees growing under elevated
CO2 have higher sap flow in wet soils but
lower sap flow in dry soils
Source: Fig. 3. Zeppel et al. 2011
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Sap Flow Versus Single Variable, e.g. VPD
Source: Fig. 3. Pfautsch et al. 2011
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Linear or Non-Linear Regression
Source: Fig 4.
Pfautsch & Adams, 2012
Simple, easy to use and interpret
Not rigorous!
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Linear or Non-Linear Regression
• Method:
• Data from non-rain days, or all data
• Allocate data to logical categories (e.g. season,
pre- and post-treatment)
• Sap flow on y-axis, variable on x-axis
• To lessen variance, average data, e.g. if
measuring at 15 min intervals, use hourly or 2-
hourly averages
• Statistical Test:
• Linear Regression
• Non-Linear Regression (logarithmic)
• Use whichever gives highest R2 value
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Linear or Non-Linear Regression
• Interpretation:
• A significant linear relationship means no, or
very little, stomatal closure to variable
• A significant non-linear relationship means
stomatal closure to variable
• No relationship means that variable is not
influencing sap flow
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Linear or Non-Linear Regression
• Example References:
• Many studies use this technique
• Pfautsch & Adams 2012. Oecologia
• Rosado et al., 2012. Agric. For. Meteor
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How Much Data to Use?
VPD (kPa)
0 1 2 3 4 5J (
cm
3 c
m-2
day
-1)
-20
0
20
40
60
80
100
Summary variable or averages All data points
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How Much Data to Use?
Summary variable or averages All data points
• You’ve collected the data so you
should use it??
• Assumptions on which data to
average or summarise may not be
logically or biologically valid
• Usually much greater variability in the
dataset
• “Cleaner”
• Easier to visualise
• Less variability
• Therefore can achieve a higher R2
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Summarising or Averaging Variables
• Hourly averages in 6-hour windows:
• e.g. Pfautsch et al. (2011).
• Windows = 10am – 4pm; and 12am – 6am
• Data measured every 10 minutes then averaged into 30 minute bins:
• e.g. Forster (2012).
• Data measured every 30 minutes then averaged into 2 hour bins:
• e.g. Duursma et al. (2011).
• Sum of diurnal data versus some maximum measurement.
• e.g. Pfautsch & Adams (2012): Sum of nightly sap flow versus nightly VPDmax
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Sap Flow Versus Many Variable
Solar Radiation (W/m2)
0 200 400 600 800
JS (
cm
3/h
r)
0
40
80
120
160
200
Solar Radiation
VPD (kPa)
0.0 0.5 1.0 1.5 2.0 2.5
JS (
cm
3/h
r)
0
40
80
120
160
200
VPD
Soil Water Content (m3/m
3)
0.090 0.095 0.100 0.105 0.110 0.115 0.120
JS (
cm
3/h
r)
0
40
80
120
160
200
Soil Water Content
Soil Water Potential (kPa)
-300 -250 -200 -150 -100 -50 0
JS (
cm
3/h
r)
0
40
80
120
160
200
Soil Water Potential
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Partial Regression
Source: Table 1, Forster 2012
Relatively simple and easy to interpret
Shows the response of one predictor while controlling for other
related predictors
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Partial Regression
• Method:
• Data from non-rain days, or all data
• Sap flow is the dependent variable, there can be
multiple independent variables but only choose
variables which are meaningful
• To lessen variance, average data, e.g. if
measuring at 15 min intervals, use hourly or 2-
hourly averages
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Partial Regression
• Method (cont.):
• A statistical package, e.g. SPSS, is needed:
• ANALYSE > REGRESSION > LINEAR - then
insert your dependent and independent
variables and make sure that "Method:" is set to
"Enter". Then click on STATISTICS > make
sure that the "part and partial correlations
box is ticked" > press continue. Now click
PLOTS > tick the "produce partial plots" box >
CONTINUE. Now click OK and the model will
run.
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Partial Regression
• Method (cont.):
• Find the results in the Partial Correlation table
(in SPSS this is in the coefficients table)
• Partial R2 = the square of the partial correlation
multiplied by 100
• VPD Partial corr. = 0.682
• Partial R2 = (0.682 * 0.682) * 100 = 46.518%
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Partial Regression Plot Source: Adapted from
Table 1, Forster 2012
Tree Sap Flow
-100 -80 -60 -40 -20 0 20 40 60 80 100
Gal
l S
ap F
low
-3
-2
-1
0
1
2
3
Solar Radiation
-400 -200 0 200 400 600
Gal
l S
ap F
low
-3
-2
-1
0
1
2
3
Temperature
-10 -8 -6 -4 -2 0 2 4 6 8
Gal
l S
ap F
low
-3
-2
-1
0
1
2
3
VPD
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
Gal
l S
ap F
low
-3
-2
-1
0
1
2
3
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Partial Regression
• Interpretation:
• The variance explained is a clear quantitative
indicator of which variable is most important
while taking into account all other variables
• A univariate linear regression analysis may find
a significant relationship between 2 variables
(e.g. solar radiation and VPD), but a multivariate
linear regression analysis will tell you which is
more important
• The partial slope or correlation indicates
whether the relationship is positive or negative
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Partial Regression
• Example References:
• Taylor & Eamus, 2008. Tree Phys.
• Forster, 2012. Fungal Ecology.
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Generalized Additive Model
Source: Fig 3.
Duursma et al. 2011
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• Method:
• Type of regression analysis of sap flow (y-axis)
against an environmental variable, e.g. VPD or
solar radiation, (x-axis)
• See Wood (2006) for more details
• Dendrometers (DBL60 Band Dendrometer)
• Statistical Test:
• Smoothed regression with 95% C.I.
• Example References:
• Duursma et al., 2011, Tree Phys.
Generalized Additive Model
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Source: Fig 3.
Forster 2012
Normalising Data
• Sap flow data can be of
different magnitudes
• Typical comparison: roots
versus trunk; small versus
large tree
• Display data on different axes
or normalise data
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Normalising Data
Source: Fig 4.
Eller et al. 2013
• Method:
• Sap velocity data
• Find the maximum value (careful with
erroneous data, including spikes or noise)
• Calculate percentage based on this
maximum value
• Statistical Test:
• Visual Inspection
• Repeated Measures ANOVA
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Normalising Data
Source: Fig 4.
Eller et al. 2013
• Interpretation:
• If direction and magnitude are the same
then the hydraulic behaviour or
architecture is the same
• Example Reference:
• Eller et al., (2013) New Phytologist
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Only HRM and HFD can measure reverse sap flow
Hydraulic Redistribution – Reverse Flow
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Hydraulic Redistribution
Figure from Oliveira et al..2005
Typically, visual inspection of data only
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Hydraulic Redistribution
Source: Fig. 6. Oliveira et al. (2005)
Typically, visual inspection of data only – average of night time values
Flow to
Trunk
Flow to
Lower
Soil
Dry Season Wet Season
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Hydraulic Redistribution & Schematics
A complicated story…
Distal Sensor on Lateral Root
Proximal Sensor on Main Root
Source: Fig. 7. Bleby et al. (2010)
Distal Sensor on Lateral Root
Proximal Sensor on Main Root
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Hydraulic Redistribution & Schematics
… can be simplified with a schematic
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Source: Fig. 2 Nadezhdina et al. (2009)
Hydraulic Redistribution & Schematics
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Source: Fig. 2 Nadezhdina et al. (2009)
Hydraulic Redistribution & Schematics
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Source: Figs. 5, Nadezhdina et al. (2009)
Hydraulic Redistribution & Xylem Depth
Northern Root = Black Line
Southern Root = Grey Line
Typically, average data are presented…
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Hydraulic Redistribution & Xylem Depth
… but with Sap Flow Tool, you can show hydraulic redistribution pattern over
the entire xylem depth (radial profile)
Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12
Irrigation
Event
Bark
Heartwood
Green =
Reverse
Flow
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Hydraulic Redistribution & Xylem Depth
Sap Flow Tool Demonstration
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Hydraulic Redistribution
• Notes:
• You can use either heat velocity, sap velocity or
sap flow data
• CRITICAL: YOU MUST ENSURE YOU HAVE
MEASURED ZERO FLOW ACCURATELY
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Circumferential Data – 2D Figure
Source: Fig 5. Cermak et al. 2004
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Circumferential Data – 2D Figure
4 sensors installed at
cardinal points
Divide tree into 4
segments
Find maximum for
each segment
North
East
South
West
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Circumferential Data – 3D Figure
Source: Fig 5. Cermak et al. 2004
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Fre
qu
ency
of
J S P
eak
Tim
e (%
)
0
4
8
12
16
20
24
28
Hours
8 10 12 14 16 18 20
0
4
8
12
16
20
24
28
0
4
8
12
16
20
24
28 E. cladocalyx
E. melliodora
E. polybractea
JS Peak Time
• Method:
• Data from non-rain days
• Usually summer data
• You can focus on a single month
• Sort data into hour or half-hourly bins
• Determine a frequency for each bin
• Statistical Test:
• Comparing single bin: ANOVA
• Comparing all data: Repeated Measures
ANOVA
Source: Fig 4. Doronila & Forster in press
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JS Peak Time Demonstration
JS Peak Time
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Fre
qu
ency
of
J S P
eak
Tim
e (%
)
0
4
8
12
16
20
24
28
Hours
8 10 12 14 16 18 20
0
4
8
12
16
20
24
28
0
4
8
12
16
20
24
28 E. cladocalyx
E. melliodora
E. polybractea
JS Peak Time
• Interpretation:
• Uni-modal data means there is an optimal time
for stomatal opening
• Multi-modal data means stomata are sensitive
to VPD
• Early peak means stomata close early in day.
Does early stomatal closure leads to less CO2?
Source: Fig 4. Doronila & Forster in press
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JS Peak Time
• Related Measurements:
• Stomatal conductance (SC-1 Leaf Porometer)
• Photosynthetic Rate (CI-340 from CID)
• Dendrometers (DBL60 Band Dendrometer)
• Example References:
• Doronila & Forster, in press, Int. J. Phyt. Rem.
• Du et al. 2011. Agric. For. Meteor.
Source: Fig 5.Du et al. 2011
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Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8
JS Peak Time and VPDmax
E. cladocalyx
E. melliodora
E. polybractea
Source: Fig 3.
Doronila & Forster in press
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JS Peak Time and VPDmax
Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8 • Method:
• Data from non-rain days
• Usually summer data
• You can focus on a single month
• VPDmax = maximum VPD for a diurnal period
• JS,max = peak sap flow for same diurnal period
• Statistical Test:
• Linear or Non-Linear Regression
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Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8
JS Peak Time and VPDmax
• Interpreting Data:
• High VPD day
• Mid-summer of Heat-wave
• Early closure of stomata
• Peak JS early in the day
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Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8
JS Peak Time and VPDmax
• Interpreting Data:
• High VPD day
• Mid-summer of Heat-wave
• Late closure of stomata
• Peak JS late in the day
• Unlikely scenario
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Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8
JS Peak Time and VPDmax
• Interpreting Data:
• “Normal” VPD day
• Typical, sunny day
• Little to no stomatal closure
• Peak JS around midday
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Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8
JS Peak Time and VPDmax
• Interpreting Data:
• Low VPD day
• Cool, cloudy day
• Late opening of stomata
• Peak JS late in the day
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JS Peak Time and VPDmax
Time of JS,max
08:00:00 10:00:00 12:00:00 14:00:00 16:00:00 18:00:00
VP
Dm
ax (
kP
a)
0
1
2
3
4
5
6
7
8 • Related Measurements:
• PSY1 Stem Psychrometer
• SC-1 Leaf Porometer
• SMM Soil Moisture Meter
• Example Reference:
• Doronila & Forster, in press, Int. J. Phyt. Rem.
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JS and Optimal VPD or Temperature
10
20
30
40
50
AB A AB CD CD BC CD D CD
Tem
pera
ture
(
C)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
0
1
2
3
4
5
6
7
AB A ABC DE DE BCD DE E CDE
VP
D (
kP
a)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
(a)
(b)
• Reference:
• Doronila & Forster, in press, Int. J. Phyt Rem.
• Definition:
• The optimal VPD or temperature for the
maximum rate of sap velocity
• At what value of VPD or temperature is a plant
the most happiest
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JS and Optimal VPD or Temperature
10
20
30
40
50
AB A AB CD CD BC CD D CD
Tem
pera
ture
(
C)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
0
1
2
3
4
5
6
7
AB A ABC DE DE BCD DE E CDE
VP
D (
kP
a)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
(a)
(b)
• E. cladocalyx:
• VPD: 2.6 kPa
• Temperature: 26.2
C
• E. melliodora:
• VPD: 2.1 kPa
• Temperature: 23.9
C
• E. polybractea:
• VPD: 2.0 kPa
• Temperature: 23.2
C
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JS and Optimal VPD or Temperature
10
20
30
40
50
AB A AB CD CD BC CD D CD
Tem
pera
ture
(
C)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
0
1
2
3
4
5
6
7
AB A ABC DE DE BCD DE E CDE
VP
D (
kP
a)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
(a)
(b)
• Method:
• Data collection should be done over an
extensive time period in order to capture
varying VPD and temperature
• Other environmental variables, particularly soil
moisture, are assumed to be optimal
• Take JS data and sort from highest to lowest
• Remove the lowest 95% of values
• Keep highest 5% of values for analysis
• Note: 5% is an arbitrary value
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Data Manipulation Demonstration
JS and Optimal VPD or Temperature
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JS and Optimal VPD or Temperature
10
20
30
40
50
AB A AB CD CD BC CD D CDT
em
pera
ture
(
C)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
0
1
2
3
4
5
6
7
AB A ABC DE DE BCD DE E CDE
VP
D (
kP
a)
EC2 EC5 EC7 EM5 EM7 EM9 EP3 EP5 EP8
(a)
(b)• Statistical Test: One-Way ANOVA with a Tukey’s HSD post-hoc test
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JS, VPD and Hysteresis
Source: Fig 3.
Pfautsch & Adams 2012
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Hysteresis Definition
• The lagging of an effect behind its cause
• “Wetting” and “Drying” curves differ
• When relating one variable to another, you
must declare whether you are on the
wetting or drying curve
Source: http://jan.ucc.nau.edu/~doetqp-p/courses/env302/lec18/LEC18.html
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0.0 0.5 1.0 1.5 2.0 2.5 3.0
JS (
cm
3/h
r)
0
5
10
15
20
25
30
8am
9am
10am
11am12pm1pm
2pm
3pm4pm
5pm
6pm
7pm8pm
Hysteresis Definition
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• Method:
• Data from selective days, e.g. prior, during and
post-treament
• VPD on x-axis
• JS = on y-axis
• Statistical Test:
• Usually visual inspection
• Curve fitting procedure?
JS, VPD and Hysteresis
VPD
0.0 0.5 1.0 1.5 2.0 2.5 3.0
JS (
cm
3/h
r)
0
5
10
15
20
25
30
8am
9am
10am
11am12pm1pm
2pm
3pm4pm
5pm
6pm
7pm8pm
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• Interpreting Data:
• Different shape curves for
different treatments
JS, VPD and Hysteresis
VPD
0.0 0.5 1.0 1.5 2.0 2.5 3.0
JS (
cm
3/h
r)
0
5
10
15
20
25
30
IRRIGATED
DROUGHT
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Source: Fig 3.
Pfautsch & Adams 2012
JS, VPD and Hysteresis
Early
Summer
Mid
Summer Heatwave Recovery
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Nocturnal Sap Flow
• What is the definition of “night”?
• If you have access to a solar radiation sensor, night is defined as values >1
or > 2 W/m2
• Arbitrary designation of night – e.g. Midnight to 6am (Pfautsch et al. 2011)
• Arbitrary designation of night – 1 hour post-sunset to 1 hour prior-sunrise
where sunset and sunrise times are collated from some official website or
database
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Nocturnal Sap Flow
- Nocturnal sap velocity as a percentage of
maximum day-time rate (e.g. Rosado et al.,
2012)
• Corrects for differences in plant or stem size
• Calculations can be based on heat velocity or
sap velocity data
• Over what time period are measurements
taken? e.g. is maximum day-time rate
calculated over a 12 month, 1 season, 1 week
period??
• Is it biologically or physiologically meaningful?
Source: Fig 3.
Rosado et al. 2012
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Nocturnal Sap Flow
- Nocturnal sap velocity as a percentage of dry,
day-time summer rates measured at noon (e.g.
Dawson et al., 2007)
• Corrects for differences in plant or stem size
• Calculations can be based on heat velocity or
sap velocity data
• Assuming this period is the highest velocity the
plant will exhibit
• Is it biologically or physiologically meaningful?
Source: Fig 1.
Dawson et al. 2007
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Nocturnal Sap Flow
- Nocturnal sap flow as a proportion of diurnal sap flow (e.g.
Pfautsch et al., 2011)
• i.e. ΣQnight divided by ΣQday
• No correction for differences in plant or stem size
• Calculations must be based on corrected, sap flow data
• No consensus on how many days/nights need to be sampled
• Integrating the entire day-time and night-time period
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Nocturnal Sap Flow
- Nocturnal sap flow as a proportion of total daily sap flow (e.g.
Forster, submitted)
• i.e. ΣQnight divided by ΣQtotal
• No correction for differences in plant or stem size
• Calculations must be based on corrected, sap flow data
• No consensus on how many days/nights need to be sampled
• Integrating entire night-time with total diurnal period
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