Beyond fractals: surrogate time series and fields Victor Venema and Clemens Simmer Meteorologisches Institut, Universität Bonn, Germany Cloud measurements: Cloud measurements: Susanne Crewell, Ulrich Löhnert Susanne Crewell, Ulrich Löhnert , Sebastian Schmidt , Sebastian Schmidt Climate data & analysis: Climate data & analysis: Susanne Bachner, Alice Kapala, Henning Rust Susanne Bachner, Alice Kapala, Henning Rust Radiative transfer & analysis: Radiative transfer & analysis: Sebastián Gimeno García , Anke Kniffka, Sebastián Gimeno García , Anke Kniffka, Steffen Meyer, Sebastian Schmidt Steffen Meyer, Sebastian Schmidt 3D cloud modelling: 3D cloud modelling: Andreas Chlond, Frederick Chosson, Andreas Chlond, Frederick Chosson, Siegfried Raasch, Michael Schroeter Siegfried Raasch, Michael Schroeter
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Beyond fractals: surrogate time series and fields Victor Venema and Clemens Simmer Meteorologisches Institut, Universität Bonn, Germany Cloud measurements:
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Beyond fractals: surrogate time series and fields
Victor Venema and Clemens Simmer
Meteorologisches Institut, Universität Bonn, Germany
Cloud measurements: Cloud measurements: Susanne Crewell, Ulrich Löhnert Susanne Crewell, Ulrich Löhnert , Sebastian Schmidt, Sebastian Schmidt
Climate data & analysis:Climate data & analysis:Susanne Bachner, Alice Kapala, Henning RustSusanne Bachner, Alice Kapala, Henning Rust
Radiative transfer & analysis: Radiative transfer & analysis: Sebastián Gimeno García , Anke Kniffka, Sebastián Gimeno García , Anke Kniffka,
Steffen Meyer, Sebastian SchmidtSteffen Meyer, Sebastian Schmidt3D cloud modelling:3D cloud modelling:
Andreas Chlond, Frederick Chosson, Andreas Chlond, Frederick Chosson, Siegfried Raasch, Michael SchroeterSiegfried Raasch, Michael Schroeter
Clouds are not spheres, mountains are not cones,
coastlines are not circles, and bark is not smooth, nor does
lightning travel in a straight line
Benoit B. Mandelbrot in The Fractal Geometry of Nature (1983)
Fractals
Implied: nature is fractal Fractal, self-similar
– Zoom in, looks the same– Structure measure is a power law of scale– Linear on a double logarithmic plot
Beginning of complex system sciences? Structure on all scales
My experience: good approximation for turbulence and stratiform clouds, but often see different signals
The great tragedy of science — the slaying of a beautiful theory by
an ugly fact
Thomas Henry Huxley (1825–1895)
Content
Motivation – What I do– Radiative transfer through clouds– Basic algorithm
Case study – 3D clouds Validation - 3D clouds Structure functions of surrogates
Motivation – compare multifractals Conclusions More information
Motivation – Cloud structure
Motivation – Cloud structure
Motivation – Cloud structure
Motivation – Cloud structure
Motivation Can not measure a full 3D cloud field Need 3D field for radiative transfer calculations Can measure many (statistical) cloud properties Generate cloud field based on statistics
measurements
Nonlinear processes– Precise distribution
Non-local processes– E.g. power spectrum (autocorrelation function)
In geophysics you generally do not have full fields, but can estimate these two statistics
Time series
The iterative IAAFT algorithmSchreiber and Schmitz
DistributionFlow diagram Time series
Case study
Two flights: Stratocumulus, Cumulus Airplane measurements
– Liquid water content– Drop sizes
Triangle horizontal leg (horizontal structure) A few ramps, for vertical profile
Three cloud generators Irradiance modelling and measurement
Surrogates from airplane data
Three reconstructions
Irradiances stratocumulus
Irradiances cumulus
0.0 0.2 0.40.0
0.1
0.2
0.3
0.4
0.5 aircraft measurement
CLABAUTAIR MC IPA
PD
F(F
)
F [W m-2 nm-1]0.0 0.2 0.4
0.0
0.1
0.2
0.3
0.4
0.5SITCOM
MC IPA
F [W m-2 nm-1]0.0 0.2 0.4
0.0
0.1
0.2
0.3
0.4
0.5 MODIS cloud cover & Reff
MO
DIS
clo
ud c
over
(60
%)
IAAFT MC IPA
F [W m-2 nm-1]
0.0 0.5 1.00.0
0.1
0.2CLABAUTAIR
MC IPA
ground measurement
PD
F(F
)
F [W m-2 nm-1]0.0 0.5 1.0
0.0
0.1
0.2SITCOM
MC IPA
F [W m-2 nm-1]0.0 0.5 1.0
0.0
0.1
0.2M
OD
IS c
loud
cov
er &
Re
ffIAAFT
MC IPA
F [W m-2 nm-1]
MO
DIS
clo
ud c
over
(60
%)
0.0 0.2 0.40.0
0.1
0.2
0.3
0.4
0.5 aircraft measurement
CLABAUTAIR MC IPA
PD
F(F
)
F [W m-2 nm-1]0.0 0.2 0.4
0.0
0.1
0.2
0.3
0.4
0.5SITCOM
MC IPA
F [W m-2 nm-1]0.0 0.2 0.4
0.0
0.1
0.2
0.3
0.4
0.5 MODIS cloud cover & Reff
MO
DIS
clo
ud c
over
(60
%)
IAAFT MC IPA
F [W m-2 nm-1]
0.0 0.5 1.00.0
0.1
0.2CLABAUTAIR
MC IPA
ground measurement
PD
F(F
)
F [W m-2 nm-1]0.0 0.5 1.0
0.0
0.1
0.2SITCOM
MC IPA
F [W m-2 nm-1]0.0 0.5 1.0
0.0
0.1
0.2M
OD
IS c
loud
cov
er &
Re
ffIAAFT
MC IPA
F [W m-2 nm-1]
MO
DIS
clo
ud c
over
(60
%)
Validation – 3D clouds
3D models clouds -> 3D surrogates Full information, perfect statistics Test if the statistics are good enough
The root-mean-square (RMS) differences are less than 1 percent (not significant)
Significant differences– Fourier surrogates: distribution is important– PDF surrogates: correlations are important
Trivial problem, but just numerical result
“Validation” time series
1D climate time series and clouds 4th order structure function
– Surrogates more accurate (as multifractal)
Full information, perfect statistics Numerical test how good the statistics are