Lecture 2:
Modeling of Land Surface Phenology with
satellite imagery
Kirsten M. de Beurs, Ph.D.
Assistant Professor of Geography
Center for Environmental and Applied Remote Sensing (CEARS)
Virginia Polytechnic Institute and State University
Kdebeurs@vt.edu
http://www.mapseasons.net
Madison LSP Workshop: 08 APR 2008
Southwest Virginia
Northeastern Maine
Death Valley
Corn/Soy belt Central Illinois
Tundra Northern Alaska
Phenological Metrics
• Phenological metrics describe the phenology
of vegetation growth as observed by satellite
imagery.
• Standard metrics derived are:
–
–
–
–
Onset of greening
Onset of senescence
Timing of Maximum of the Growing Season
Growing season length
• However, there are many more metrics
available.
Maximum NDVI
Time
Integrated
NDVI
Start of Season
Duration of Season
SOS
End of Season
Phenological Metric 
Phenological Interpretation
• Time of SOS (EOS):
beginning (end) of measurable photosynthesis.
• Length of the growing season:
duration of photosynthetic activity.
• Time of Maximum NDVI:
time of maximum photosynthesis.
• NDVI at SOS (EOS):
level of photosynthetic activity at SOS (EOS).
• Seasonal integrated NDVI:
photosynthetic activity during the growing season.
• Rate of greenup (senescence):
speed of increase (decrease) of photosynthesis.
Ground Validation
• It is desirable to compare the satellite
derived phenological estimates with data
observed at ground level.
• However this is not a trivial task due to:
– Large pixel sizes of satellite imagery.
– Composited data.
• Thus, it is often unclear what LSP metrics
actually track.
Four Categories:
• A diversity of satellite measures
and methods has been developed.
• The methods can be divided into four
main categories:
–
–
–
–
Threshold
Derivatives
Smoothing Algorithms
Model fit
Thresholds
0.8
0.7
NDVI
0.6
0.5
0.4
0.3
0.2
0.1
0
J
F
M
A
M
J
J
A
S
O
N
D
Months
When do you estimate that the growing
season starts?
Thresholds
0.8
0.7
NDVI
0.6
0.5
0.4
0.3
0.2
0.1
SOS
EOS
0
J
F
M
A
M
J
J
A
S
O
N
D
Months
• Simplest method to determine SOS and EOS.
• Threshold is arbitrarily set at a certain level (e.g. 0.09, 0.17, 0.3 etc).
Thresholds
• Measure is easy to apply.
• However, across the conterminous US,
NDVI threshold can vary from 0.08 to
0.40.
• Thus, it is inconsistent when applied
towards large areas.
Thresholds based on NDVI ratios
• First, translate NDVI to a ratio based
on the annual minimum and maximum:
NDVIratio = (NDVI-NDVImin)
/
(NDVImax-NDVImin)
1
0.6
0.4
0.2
0
J
F
M
A
M
J
J
A
S
O
N
D
Months
1
0.8
NDVI
NDVIratio
NDVIratio
NDVI
0.8
0.6
0.4
0.2
0
J
F
M
A
M
J
J
A
Months
S
O
N
D
1
• 50% is the most often
used threshold.
• The increase in
greenness is believed
to be most rapid at
this threshold.
NDVIratio
0.8
0.6
0.4
0.2
0
J
F
M
A
M
J
J
A
S
O
N
1
Months
0.8
NDVIratio
• Some believe that rapid
growth is more
important than first
leaf occurrence or bud
burst.
• Lower likelihood of soil
– vegetation confusion
than at lower
thresholds.
D
0.6
0.4
0.2
0
J
F
M
A
M
J
J
A
Months
S
O
N
D
50% Threshold (Seasonal Mid-point)
(White et al., mean day = 124, May 4th)
Derivatives
• What is a derivative?
• What is the slope of this line?
• Why?
60
50
40
30
20
10
0
0
5
10
15
20
30
25
20
15
10
5
0
0
5
10
15
-1 0
5
10
15
20
5
4
3
2
1
0
-2
-3
-4
-5
20
1
Local
Derivative
NDVI
0.8
0.6
0.4
Derivative is
calculated based
on 3 composites.
0.2
0
J
F
M
A
M
0.011
J
J
A
S
O
N
D
Months
Derivative
0.006
0.001
-0.004
J
F
M
A
M
J
J
A
-0.009
Months
S
O
N
D
(Week 3 – Week 1) /
(difference in
days)
SOS: day where
derivative is
highest
EOS: day where
derivative is lowest
0.8
0.7
NDVI
0.6
0.5
0.4
0.3
0.2
0.1
0
J
F
M
A
M
0.011
J
J
A
S
O
N
D
S
O
N
D
Months
0.009
Derivative
0.007
0.005
0.003
0.001
-0.001
-0.003
J
F
M
A
M
J
J
A
-0.005
Months
Smoothing Algorithms
• Autoregressive moving average
• Fourier analysis
Autoregressive moving average
• Frequently used method developed in
the early 1990’s by Dr. Brad Reed.
• Works similarly as the thresholds
method, however the threshold is
established by a moving average.
• What is a moving average?
Autoregressive moving average
0.9
0.8
0.7
NDVI
• You take the
average of a
certain number of
time periods.
• Each time period
you shift one over.
0.6
0.5
0.4
0.3
0.2
0.1
0
J
F
M
A
M
J
J
A
Months
S
O
N
D
Autoregressive moving average
• The time lag used to calculate the
forward and backward looking curves is
arbitrarily chosen.
• Brad Reed (1994) used a time lag of 9
composites.
• In case of shorter seasons (semi-arid
Africa) shorter time lags have been
used (~2 months or 4 composites).
Archibald and Scholes (2007).
Archibald and Scholes (2007).
Limitations of the moving average
method
• How would the moving average curve
look in case of a major disturbance?
• The method does not work in case of
multi-peak growing seasons.
• There are no clear criteria regarding
the selection of the delay time.
Fourier Analysis
• Fourier analysis approximates
complicated curves with a sum of
sinusoidal waves at multiple frequencies.
• The more components are included the
more the sum approximates the signal.
• In phenological
studies:
– Amplitude:
variability of
productivity
– Phase: measures
the timing of
the peak.
de Beurs and Henebry, 2008
Limitations of Fourier Analysis
• The Fourier composites do not necessarily
have an ecological interpretation.
• This approach is only useful for a study region
that you know really well.
• The method requires long time series, with
observations that are equally spaced.
• Missing values (clouds!) have to be filled.
• NDVI signals are typically not exactly
sinusoidal, so it is necessary to fit several
terms.
Complicated
adjustments
High order
annual
splines
with
roughness
dampening.
Hermance et al. 2007
Bradley et al 2007
Model fit
• Models based on growing degree days
• Logistic Models
• Gaussian Local Functions
Growing Degree Days
• Development rate of plants and insects is
temperature dependent.
• A plant develops quicker at a higher temperature.
• Daily temperature readings can be used to calculate
growing degree-days
• Growing degree days are a measure of accumulated
heat.
• Idea was first introduced in 1735 by Reaumur.
Growing Degree Days
• Accumulated temperature is now recognized
as the main factor influencing year-to-year
variation in phenology.
• Photoperiod alone, without the interaction
with temperature, cannot explain the annual
variability of phenology at a given location.
• Photoperiod is the same in each year.
Intercept:
NDVI at the start of the
observed growing season.
Start of Season:
First composite included in
the best model.
NDVI peak height:
NDVI at peak NDVI.
Green-up period (DOY):
Translated from
accumulated relative
humidity, the number of
days necessary to reach
peak NDVI
NDVI    AGDD  AGDD2
o Intercept: α

o Green-up period

2
peak position (%hum):
o NDVI peak height:
2

4
Logistic Models
• Straightforward logistic model
• a and b are empirical coefficients that are associated
with the timing and rate of change in EVI.
• c+d combined give the
c potential maximum value
EVI t  
d
1 e
• d presents the minimum
value (the background EVI
value).
• This model can be
approximated with
numerical methods such as
Levenberg-Marquardt
a  bt
Zhang, 2004
c
EVI t  
d
a  bt
1 e
Onset_Greenness_Increase
Onset_Greenness_Maximum
Onset_Greenness_Decrease
Onset_Greenness_Minimum
NBAR_EVI_Onset_Greenness_Minimum
NBAR_EVI_Onset_Greenness_Maximum
NBAR_EVI_Area
days since 1 January
days since 1 January
days since 1 January
days since 1 January
NBAR EVI value
NBAR EVI value
NBAR EVI area
2000
2000
2000
2000
16-bit
16-bit
16-bit
16-bit
16-bit unsigned
16-bit unsigned
16-bit unsigned
MODIS/Terra Land Cover Dynamics Yearly L3 Global 1km SIN Grid: MOD12Q2
Gaussian Local Functions

  t  a  a3 
1
exp  
 , if t  a1
a

  2  

NDVI  c1  c 2 
  a  t  a5 

1
exp   a  , if t  a1
  4  


The upper part of the equation
is fitted to the right half of
the time series.
The lower part of the equation
fits to the left half of the
time series.
a2 and a4: the width of the
curves
a3 and a5: the flatness (or
kurtosis) of the curves
Jönsson and Eklundh, 2002 and Jönsson and
Eklundh, 2004
c1 and c2: base parameters determine the
intercept and the amplitude of the curves,
respectively.
a1: the timing of the maximum (measured in
time units).
Gaussian Local Functions
• Applied in a program called TIMESAT
http://accweb.nascom.nasa.gov/data/
MODIS phenology for
the North American
Carbon Program
Annual phenology data
based on:
– NDVI, EVI, LAI or
FPAR
• Spatial resolution:
250m or 500m
Phenology data include:
greenup date, browndown date, length of growing season,
minimum NDVI, date of peak NDVI, peak NDVI, seasonal
amplitude, greenup rate, browndown rate, seasonal
integrated NDVI, maximum NDVI during the year, quality
control map, land cover map.