Transcript Applications of Modern Data Collection and Modelling Techniques

Applications of Modern Data
Collection and Modelling
Techniques to Biogeochemistry
GGR 403S
Eugene Kwan
March 2004
The Scientific Method
question
hypothesis
do experiments
data acquisition
think about results
data analysis
explain the results
data modelling
predict the future
data extrapolation
Data Acquisition
• Remote Sensing
• Isotopic Proxy Data/Mass Spectrometry
• Eddy Correlation Techniques
Remote Sensing
• Satellites, Airplanes, Ground-Based
• Uses spectrometers: instruments which
analyze different parts of the
electromagnetic spectrum
• “Passive vs. Active” Sensing
– passive: satellite just gathers light
– active: satellites emit energy
Satellite Orbits
• Geostationary: satellite stays over the
same part of the Earth at all times
• Near-Polar: N/S orbits which, with the
Earth’s E/W rotation, allow broad coverage
• Sun-Synchronous: Each area of the world
is covered at the same local sun time
Some Terminology
• “swath”: the area on the surface a satellite can image at
one time
• “spatial resolution”: the size of the smallest feature that
can be detected
• “spectral resolution”: how far apart two spectral features
must be in wavelength to be distinguished
• “radiometric resolution”: how far apart two signals have
to be in amplitude to be resolved
Types of Sensing
• Optical/Stereoimages
• Multi-Spectral
• Thermal
• Weather
• Land-Observation
Stable Isotope Ratio
Mass Spectrometry
• “proxy data”: a series of measurements which
from which various historical parameters may be
inferred
e.g. temperature may be inferred from
oxygen isotope ratios in carbonates
• typically used to reconstruct past climates
A Quick Review
• Atoms contain protons (positive charge),
neutrons (no charge), and electrons (negative
charge)
• The chemical properties of an atom depend
principally on its atomic number: the number of
protons
• Atoms are neutral:
# protons = # electrons
Isotopes
• Isotope:
- same number of protons and electrons
- different number of neutrons
- e.g. 16O and 18O are isotopes
• absolutely not to be confused with allotrope,
isomer, etc.
• Stable vs. Unstable: unstable isotopes decay
into stable ones over time
(e.g. 13C decays and is unstable while 12C does
not decay and is stable)
Isotopic Composition
• elements naturally exist in a distribution of
isotopic forms: natural abundance
• non-equilibrium biological or physical
processes can alter this distribution:
fractionation
e.g. Plant Photosynthesis
plants prefer 12C over 13C by…
C3 plants 16-18%
C4 plants 4%
Carbon Isotopic Composition
• ref.: Coplen. Nature. 1995, 375, 285.
 C
 C
-  12 
 12 
C
C



reference
sample
13
δ C=
×1000
13
 C
 12 
 C reference
13
13
• Reference is with respect to a special carbonate rock
(NBS-19)
Measuring Isotopes with
Mass Spectrometry
1)
Sample is vaporized.
2)
The gas is ionized, sometimes by bombarding it with
electrons.
3)
A magnetic field is used to separate the ions by
mass:charge (m/z) ratio.
4)
A detector measures the relative abundance of each
m/z: gives a mass spectrum
- technique is extremely sensitive
Missing Carbon Sink
• carbon isotope fractionation can be used
to distinguish between carbon dioxide
fluxes between the land and oceans
• ocean-atmosphere CO2 exchange:
– insignificant fractionation
• on-land CO2 partitioning:
– should result in noticeable d13C
Eddy Correlations
• used to measure pollutant fluxes in the
atmosphere
• satellite measurements:
– tend to measure total vertical concentrations
(“atmospheric column”)
– insufficient spatiotemporal resolution to calculate flux
• “flux”: how much of something passes through a
unit area per unit time
Fluid Flows
• two regimes: laminar and turbulent
• flows are empirically characterized by their
Reynold’s Number Re:
mean flow speed
Re =
UL
length scale of flow

kinematic viscosity
transition zone
laminar flow
turbulent
Re
0
1
2
3
4
5
6
7
8
9
powers of ten
atomospheric flows
generally turbulent
Turbulent Flux
• Mathematically,
flux
concentration
of pollutant X
F = na CX w
vertical
windspeed
number density of air
"air pressure"
• CX and w fluctuate, so F fluctuates
Eddy Correlation Method
flux of
pollutant X
short bar = take
average of
long bar = "take
covariance of"
F = na (Cw + C’w’)
turbulent flux
mean advective flux
decompose into
mean and fluctuating
components
C(t) = C + C'(t)
fluctuating
components
w(t) = w + w'(t)
mean components
by definition zero
by measuring C and w together quickly, we can get F
Data Analysis
• “time series”: a set of measurements collected
over time
Techniques:
- Smoothing
- Detrending
- Correlation/Autocorrelation/Convolution
- Fourier Transform (FT)
Data Smoothing
•
•
data typically too noisy to work with
would like to smooth it so trends can be
observed
Two Methods:
1) Running Average/Running Mean
2) Running Median
Running Mean
• visualization of a three-point running mean:
ruler moved along
one point at a time
imagine data
as numbers on
a strip of paper
ruler
10/3...
4
1
2
7
Q: What's your mean?
A: 7/3
becomes first point
of new smoothed series
7/3
0
8
2
3
8
Running Median
• Problem: what if there are there are
anomalous spikes in the data?
• outliers can totally swamp the average
• Solution: use a running median
reminder: median means “what’s the middle
number”? (even number of points?
average the middle two)
Example of Running Smoothing
Raw Data : Magnetic
Running
Field
46540
Mean
3 pt
46540
Magnetic Field
46520
46500
46480
46460
46500
46480
46440
0
0.5
1
1.5
Time
2
2.5
3
years
46460
-magnetic observatory data
courtesy Prof. Milkereit
0
-graphs generated in
Mathematica (by me)
-although mean appears as good
as median, a spectral analysis
(see later) will show lower S/N
0.5
1
1.5
Time
Running
years
Median
2
2.5
3
2.5
3
3 pt
46540
46520
Magnetic Field
Magnetic Field
46520
46500
46480
46460
0
0.5
1
1.5
Time
2
years
Correlation Methods
• purposes:
1) find periodicities in data
2) relate two data sets
3) subtract instrumental effects
Methods:
- auto- and cross- correlation
- convolution
Autocorrelation
•Consider a discrete time series:
f[t] = { f[t0], f[t0+D], f[t0+2D], … }
where D is the sampling interval.
Autocorrelation tries to determine how
f[t] is related to f[t-D], f[t-2D], …
If f[t] depends on f[t-nD], n=integer, then f[t] is
“autocorrelated” with “lag time” nD.
sampling interval
f[t0+3Dt]
Dt
f[t]:
4
1
2
7
0
t0
8
autocorrelation with
lag time 4Dt
2
3
8
Meaning of Autocorrelation
• Note that a “strong autocorrelation with lag time
2Dt” means:
– choose a f[t1]
– f[t1-2Dt] is strongly related (same sign, magnitude) to
f[t1]
– does not refer to particular times in the series
this series has a strong autocorrelation with lag time 2Dt
Dt
f[t]:
2
t0
3
2
3
2
3
2
3
2
Step 1: Copy the series and place it underneath the original.
f[t]:
5
3
6
-1
1
3
4
0
7
COPY
f[t]:
5
3
6
-1
1
3
4
0
7
- facing same direction, each number lined up
Step 2: Multiply adjacent numbers, then add the products.
f[t]:
f[t]:
5
X
5
3
X
3
products:
25
9
6
X
6
36
-1
X
-1
1
X
1
1
1
3
X
3
9
insert into new series
4
X
4
0
X
0
7
X
7
MULTIPLY
16
0
49
SUM: 146
SUM: 146
new autocorrelation time series
A[t]
146
inserted at
lag number 0
Step 3: Shift time series by one time step, and repeat.
f[t]:
SHIFTED BY Dt
SHIFTED BY 2Dt
5
3
6
-1
1
3
f[t]:
5
3
6
-1
1
f[t]:
5
3
6
-1
4
0
7
3
4
0
7
3
4
0
1
7
Cross-Correlation
• Tries to find relationship between two
different time series.
• e.g., sunspot activity and oceanic primary
productivity.
• Implementation: rather than copying the
original series and calculating the shift
overlaps, calculate the shift overlaps
between the two time series.
Convolution/Deconvolution
• Mathematically more complex
• Useful for
– Combining measurements taken from
different instruments
– Distinguishing real signals from instrumental
noise
• Its opposite, decovolution, can decompose
two overlapping signals into their
components.
Data Modelling
•
•
•
•
•
One Box Model
Lifetime
First-Order Approximation
Steady States/Dynamic Equilibria
Multibox Models/General Circulation
Models
Data Extrapolation
• Will consider the carbon cycle in terms of
a simple multi-box model
• Will account for pH and solubility of carbon
dioxide in the oceans
• Will make some lifetime estimates and
other predictions