WP1: Network Construction and Analysis

We intend to improve and develop techniques for the reconstruction of complex networks from 
multidimensional climatological data. For this there are important methodological problems to solve because observations from the Earth system are typically rather short, noisy, and far from being stationary. The specific objectives of WP 1 are: 

1) A critical comparison of existing methods to infer causality from bivariate data, such as cross and partial correlation, linear, nonlinear and constrained Granger causality, coarse-grained entropy and transfer entropy, joint recurrence plots and mean conditional recurrence probability. 
2) Development of surrogate data and bootstrap methods to evaluate the statistical significance of causality estimates. Realistic null hypotheses for climate time series will be formulated, which will take  into  account  (i)  autocorrelation,  (ii)  non-Gaussian  distributions,  (iii)  unevenly  spaced timescales and, in case of multivariate problems, (iv) unequal times. Challenges (i) and (ii) can in 12 general be tackled by means of block bootstrap resampling , while problems (iii) and (iv) may require novel adaptations. 
3) Generalization of the most promising techniques for the analysis of multivariate time series in order to include various climatological parameters (temperature, pressure, precipitation, wind etc.) in  the  analysis.  Special focus  is to  infer  possible  mutual influence  of  the  connections  (which provides coupling between WP1 and WP2) and a possible time delay. 
4) Development of efficient methods related to transilience matrices and based on Lagrangian indicators to characterize mass transport across different parts of the Earth by means of transport networks. Relate them to the networks used in implementations of GCMs.  
5)  Identification  of  supernodes  (regions  with  high  degree  centrality)  and  of  significant teleconnections (long range connections) and associate them to known dynamical interrelations in the climate (e.g. between ENSO, Monsoon, which provides coupling between WP1 and WP3) and retrieve the dynamics of these features as an approach to study shifts and tipping points in the climate system (which provides coupling between WP1 and WP4 and WP5).