Center for Scientific Simulation (CSS) Advanced Methods of Time by ojp13483


									    Center for Scientific Simulation (CSS)

Advanced Methods of Time Series Analysis and
  their Application to Climate Research and
         Insurance Risk Optimisation


                   Christian Blume
                  Dr. Katja Matthes
          Physics of the Middle Atmosphere
              Institute for Meteorology

                December 15, 2009
   This report gives an overview of the main results achieved in the working group Physics
of the Middle Atmosphere at the Institute for Meteorology (Matthes, Blume, Langematz)
within the interdisciplinary work and knowledge exchange with the Institute of Mathematics
(Horenko, Kaiser). In contrast to the commonly used method of multiple linear regression
(MLR) (Bodeker, 2001), the novel methods of multivariate time series analyses developed by
(Horenko, 2008) and applied during this project allows to analyse non-linear, non-stationary,
non-markovian and multidimensional problems. The methods have been tested with strato-
spheric data from observations, reanalyses as well as data from climate model simulations. A
summary of selected results is presented in (Blume, 2009).
   The method that has been studied and applied intensely is the FEM-K-Trends-Algorithm
(Horenko, 2008; Horenko, 2009a). It has been successfully utilised to determine important
variability modes in one-dimensional time series of temperature, wind, and ozone. Trends
calculated in column ozone data agree well with results from the MLR. The FEM-K-Trends-
Algorithm was also successfully applied to clustering problems in time and space. The strong
ozone reduction (WMO, 2007) as well as the stratospheric temperature decrease (Randel,
2009; Baldwin, 2009) since 1980 was confirmed with the method.
   A further development of the clustering algorithm, the FEM-VARX-Algorithm (Horenko,
2009b), has been recently successfully tested as well. The advantage compared to the FEM-K-
Trends-Algorithm is the possibility to separate external contributions such as the QBO, solar
and seasonal cycles to the observed data. This is important to understand and separate e.g.,
anthropogenic and natural contributions in the atmosphere and make more reliable future
predictions at the end. The MLR also finds single forcing contributions but in contrast to the
FEM-VARX-Algorithm it assumes that the external factors only have a stationary and linear
influence which is certainly not true for highly non-linear processes in the atmosphere.
   Besides the aforementioned clustering approaches, an artificial neural network (ANN)
(Auer, 2008; Shannon, 1970) has also been investigated and successfully applied to obser-
vational data. The non-linear influence of anthropogenic influences has been investigated and
results have been compared to the MLR output. A reasonable influence of various external
factors on column ozone could be detected and confirms that the strong decrease of column
ozone is predominantly caused by the man-made increase of stratospheric chlorine (WMO,
2007; Baldwin, 2009).
   The next steps within this working group include the detailed comparison of observations
and chemistry climate model output (WCRP, 2009) using the FEM-K-Trends-Algorithm and
the FEM-VARX-Method. Additionally, the application of novel methods of extreme value
theory (FEM-COE) (Kaiser, 2009) are planned. We are looking forward to extend the ongoing
knowledge transfer within the Center for Scientific Simulation.


Auer, P. et al. 2008. A learning rule for very simple universal approximators consisting of a
    single layer of perceptrons. Neural Networks, 21(5), 786–795.

Baldwin, M. et al. 2009. How will the stratosphere affect climate change. American Association
    for the Advancement of Science, 316, 1576–1577.

Blume, C. et al. 2009.         CSS Figure File.

Bodeker, G. 2001. Global ozone trends in potential vorticity coordinates using TOMS and
    GOME intercompared against the Dobson network: 1978-1998. Journal of Geophysical
    Research, 106, 23,029–23,042.

Horenko, I. 2008. Finite element approach to clustering of multidimensional time series. to
    appear in Journal of Scientific Computing.

Horenko, I. 2009a. On Clustering of Non-stationary meteorological Time Series. published
    electronically in Dynamics of Atmospheres and Oceans.

Horenko, I. 2009b. On data-based identification of nonstationary factor models in turbulence
    and meteorology. submitted to Journal of Climate.

Kaiser, O. et al. 2009. On data-based analysis of extreme events in multidimensional non-
    stationary meteorological systems (manuskript in preparation).

Randel, W. et al. 2009. An update of observed stratospheric temperature trends. Journal of
    Geophysical Research, 114(d2), D02107.

Shannon, D. et al. 1970. Conditioning of Quasi-Newton Methods for Function Minimization.
    Mathematics of Computation, 24, 647–656.

WCRP. 2009. Chemistry Climate Model Validation Activity for SPARC (CCMVal). http:

WMO. 2007. Scientific Assessment of Ozone Depletion: 2006. Vol. 50. World Meteorological


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