Content. A new algorithm combining geostatistics with the surrogate data approach. Problem. Motivation. Cloud structure - nonlinear
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1 A new algorithm combining geostatistics with the surrogate data approach Victor Venema, Ralf Lindau, Tamas Varnai and Clemens Simmer Motivation Content Constrained simulation Combing surrogate and kriging New non-gaussian algorithm Results Examples Statistical properties Radiative transfer results Meteorological Institute Bonn Problem Motivation Radiative transfer is non-local Radiative transfer is strongly nonlinear Can not measure a full 3D cloud field Can measure many (statistical) cloud properties Generate cloud field based on statistics measurements How to compare Radiation point-measurements Measured microphysical cloud properties 3-Dimensional cloud field Cloud structure - nonlinear Cloud structure - nonlinear
2 Cloud structure non-local Cloud structure non-local clouds Stochastic modelling Reproduce a measured field Well-suited for clouds and 3D radiative transfer Theory: Venema et al., Tellus A, pp. -, Case study: Schmidt et al., JGR, pp. 7 7, 7 (LWP) distribution & power spectrum Geostatistical interpolation method Estimate of the mean Uncertainty in input and output Sample error Kriged field Combining kriging and surrogates Constrained stochastic simulation Typical problem for many geophysical studies Limited measurements, but need a field Specify the distribution accurately (nonlinear) Specify the spatial correlations ( non-local ) Field constrained by measurements Combining kriging and surrogates Contradicting requirements smoothes, surrogates have structure Relative to kriged field, structure adds noise Mathematical formulation is different How to combine these two worlds?
3 s & kriging - algorithm No Methodology this study Statistics ACF Calculate Statistics from sample Start kriged mean field Spectral adjustment Nudge to mean Distribution adjustment Converged? LES Measurement Kriged Field Constrained error PDF Height (km) Height (km) Height (km)... Stratocumulus validation data Height (km) Height (km) Height (km) Computed with Large Eddy Simulation (LES) We use only Liquid Water Path (LWP) D fields of column integrated amount of water in cloud droplets (g m - ) One measurement sampling - PDF Chosson, F., J.-L. Brenguier and L. Schüller, "Entrainment-mixing and radiative Transfer Simulation in Boundary-Layer Clouds", J Atmos. Res. One measurement sampling - ACF Five measurements sampling 3
4 ... Line surrogate.... Lines Autocorrelation functions Stratocumulus - Line surrogate Stratocumulus - Lines surrogate 3 with distribution adjustment with distribution adjustment - stratocumulus... Line surrogate Adjusted kriged.. Lines.... Autocorrelation function Stratocumulus - Line surrogate Distribution adjusted.... Stratocumulus - Lines surrogate Distribution adjusted
5 Conclusions Generate realistic structure conditioned on means Smaller root mean square error Point measurements on ground Less case studies needed to study 3D radiative transfer Main limitation is sampling Especially one zenith pointing instrument Noisy and biased estimate Outlook Validation 3D radiative transfer calculations Estimate the statistics Cloud mask Estimation of distribution using nearby data Apply to other problems Michael Herbst and Stefan Kollet
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