High efficiency implementation of PC and PC stable algorithms yields three-dimensional graphs of information flow for the Earth' atmosphere

Causal discovery algorithms have recently been applied to s everal climate applications. In particular, in prior work we have developed methods to recover pathways o f interaction in the global climate system, using the classicPC algorithm. However, standard implementations of the PC algorithm cannot handle the large number of variables and temporal models required for t his application. This technical report shows that a more efficient implementation of the PC algorithm can provide speed gains of a factor of 1,000 or more. This in turn enables us to calculate graphs of informat ion flow with much higher resolution grids. Furthermore, we can now for the first time ever calculate in formation flow graphs that extend over three dimensions, i.e. rather than just including one layer of the planet’s atmosphere we can now capture interactions across several height layers.