How much dust? And which dust? · A conceptual estimate of potential consequences 0.001 1 100 0.0...

$: How much dust? And which dust? · A conceptual estimate of potential consequences 0.001 1 100 0.0 0.5 1.0 1.5 2.0 2.5 3.0 size(µm) Vol.-% "dust fraction" Cutting off at fixed boundaries$
How much dust? And which dust?

From grain-size data (and bulk density)to aeolian mass fractions

Michael Dietze1

1 - GFZ German Research Centre for Geosciences, Section 5.1 Geomorphology

A (more or less) typical loess section

THE PROBLEM | ONE SOLUTION | ANOTHER SOLUTION | APPLICATION | SYNTHESIS

Michael Dietze @ GFZ Potsdam > Geomorphology Section > Sediment unmixing > Workshop on dust mass accumulation rates

A (more or less) typical loess sectionA (more or less) typical loess section




0.001 1 100

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size(µm)

Vol.-

%



A more conceptual formulation of the problem

dust(s)

other

proxi-mal

distalre-

mote

1. How much solid is there?

2. How much of it is "dust"?

3. Which types/sources are there?

4. What are its average densities?



A conceptual estimate of potential consequences

0.001 1 100

0.00.5

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size(µm)

Vol.-

%

"dust fraction" Cutting off at fixed boundaries may lead to:

- underestimation of the target fraction's total vol.-%

- contamination of the target fraction, by - tail(s) of coarser fractions - contribution of smaller fractions

- bias in the resulting time series of dust



5e−02 5e−01 5e+00 5e+01 5e+02

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23

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Grain size (µm)

Vol.−

%

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020

4060

8010

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Time/sample IDR

elat

ive c

once

ntra

tion

A simple test of the contamination hypothesis – Setup A



A simple test of the contamination hypothesis – Setup B

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Grain size (µm)

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%

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Time/sample IDR

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A simple test of the contamination hypothesis – Resulting mixed data sets

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Grain−size

Vol.−

%

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Grain−sizeVo

l.−%



A simple test of the contamination hypothesis – Resulting "dust" fractions (< 4 µm)

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Time/sample ID

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ative

con

cent

ratio

n

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true fraction

apparent fraction

true fraction

apparent fraction



One approach to tackling the problem – parametric curve fitting

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Grain−size

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%

µ1, σ1, c1µ2, σ2, c2µ3, σ3, c3

Fitting n parametric distributions (log-normal, Weibull, Gamma, ...)

Attractive, because we get unmixed time series and parametric end-member definition

But, for each sample we can get different µ, σ. So which one is the right one?

What if a sample has more than n components, or less?



Another approach to tackling the problem – eigen space based decomposition (EMMA)

Considers an entire data set as input and describes it as linear combination of eigen vectors (V) and their scores (M) plus an error matrix (E).

Based on eigen space decomposition (PCA), extended to optimisation and reduction (FA), framed by scaling to real units (EMMA).

Attractive, because we get unmixed time series and unconstrained end-member definition

MX

V

X = M V + E• T




Lumi-nescence

RLumModel

BayLum

ADmin

sandbox EMMAgeo PUMAgeo

RLumShiny

rbacon

Basic and advanced data analysis

Luminescence model implementation

Bayesian age calculations

Bayesian age depth models

Advanced age data visualisation

Age error type separation

Virtual sediment section modelling

Compositional data analysis

Age-depth to proxy uncertainty propagation

Bchron

clam




FAPCA

EMMA

Online course: micha-dietze.de/pages/r_courses.html




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0.8

Class−wise explained variance (mean = 89 %)

Class

R2

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0.85

0.95

Sample−wise explained variance (mean = 97 %)

Samples

R2

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45

67

End−member loadings

Class

Rel

ative

am

ount

s

5 15 25 35 45 55 65 75 85 95

End−member scores

Samples

Rel

ative

am

ount

s

0.0

0.2

0.4

0.6

0.8

1.0

End−member ID (mode position | explained variance)EM1 (6.1 | 23 %) EM2 (4.7 | 19 %) EM3 (1.6 | 30 %) EM4 (1 | 28 %)

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0.8

Class−wise explained variance (mean = 89 %)

Class

R2

0 20 40 60 80 100

0.70

0.85

1.00

Sample−wise explained variance (mean = 93 %)

Samples

R2

0 5 10 15

01

23

45

67

Robust end−member loadings

Class

Rel

ative

am

ount

s

Robust end−member scores

Samples

Rel

ative

am

ount

s pe

r end

−mem

ber

0 20 40 60 80 100

00

00

End−member ID (mode position | explained variance)EM1 (64 | 14 %) EM2 (74 | 27 %) EM3 (98 | 26 %) EM4 (100 | 33 %)

Deterministic mode ("I know the number of components") Robust mode ("I fully allow for parameter uncertainty")



Let's apply the technique – Welcome to a special kind of dusty deposit



So?... Some recapitulation ... And a look ahead

Aeolian deposits usually comprise a mixture of components from different sources, transport pathways and transport processes, and have undergone syn- and postdepositional alteration.





Simple, subjectively defined size boundaries inevitably introduce bias, which is why we need robust approaches to unmixing data into inhertent components.






After a decision which components represent the "dust fraction(s)" of interest, it is crucial to investigate the spatial heterogeneity (or spatial autocorrelation function of the data).







With spatially "scaled" volume percentages of distinct dust fractions, one can engage with i) removing the non-solid volume fractions (water, air), ii) propagating solid volumes to age-depth-space, and iii) robustly estimating size- and component-specific material density, to produce mass deposition rates.







With spatially "scaled" volume percentages of distinct dust fractions, one can engage with i) removing the non-solid volume fractions (water, air), ii) propagating solid volumes to age-depth-space, and iii) robustly estimating size- and component-specific material density, to produce mass deposition rates. Thanks



DARTDust Accumulation Rate Tackling

Thanks



How much dust? And which dust? · A conceptual estimate of potential consequences 0.001 1 100 0.0...

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