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| Titel |
On the construction of a time base and the elimination of averaging errors in proxy records |
| VerfasserIn |
V. Beelaerts, F. De Ridder, M. Bauwens, N. Schmitz, R. Pintelon |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250020633
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| Zusammenfassung |
| Proxies are sources of climate information which are stored in natural archives (e.g. ice-cores,
sediment layers on ocean floors and animals with calcareous marine skeletons). Measuring
these proxies produces very short records and mostly involves sampling solid substrates,
which is subject to the following two problems:
Problem 1: Natural archives are equidistantly sampled at a distance grid along their
accretion axis. Starting from these distance series, a time series needs to be constructed, as
comparison of different data records is only meaningful on a time grid. The time series will
be non-equidistant, as the accretion rate is non-constant.
Problem 2: A typical example of sampling solid substrates is drilling. Because of the
dimensions of the drill, the holes drilled will not be infinitesimally small. Consequently,
samples are not taken at a point in distance, but rather over a volume in distance. This holds
for most sampling methods in solid substrates. As a consequence, when the continuous proxy
signal is sampled, it will be averaged over the volume of the sample, resulting in an
underestimation of the amplitude. Whether this averaging effect is significant, depends on the
volume of the sample and the variations of interest of the proxy signal. Starting from the
measured signal, the continuous signal needs to be reconstructed in order eliminate these
averaging errors.
The aim is to provide an efficient identification algorithm to identify the non-linearities in
the distance-time relationship, called time base distortions, and to correct for the averaging
effects.
Because this is a parametric method, an assumption about the proxy signal needs to be
made: the proxy record on a time base is assumed to be harmonic, this is an obvious
assumption because natural archives often exhibit a seasonal cycle. In a first approach the
averaging effects are assumed to be in one direction only, i.e. the direction of the axis on
which the measurements were performed.
The measured averaged proxy signal is modeled by following signal model:
-- Δ ∫ n+12Δδ-
y(n,θ) = δ- 1Δ- y(m,θ)dm
n-2 δ
where m is the position, x(m) = Δm; θ are the unknown parameters and y(m,θ) is the
proxy signal we want to identify (the proxy signal as found in the natural archive), which we
model as:
y(m, θ) = A +∑H [A sin(kωt(m ))+ A cos(kωt(m ))]
0 k=1 k k+H
With t(m):
t(m) = mTS + g(m )TS
Here TS = 1∕fS is the sampling period, fS the sampling frequency, and g(m) the unknown
time base distortion (TBD). In this work a splines approximation of the TBD is
chosen:
∑
g(m ) = b blφl(m )
l=1
where, b is a vector of unknown time base distortion parameters, and φ is a set of
splines.
The estimates of the unknown parameters were obtained with a nonlinear least squares
algorithm.
The vessel density measured in the mangrove tree R mucronata was used to illustrate the
method. The vessel density is a proxy for the rain fall in tropical regions. The proxy data on
the newly constructed time base showed a yearly periodicity, this is what we expected
and the correction for the averaging effect increased the amplitude by 11.18%. |
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