The Liang-Kleeman information flow (LKIF) index, or rate of information transfer, is a causal method that quantifies causal links between variables, and thus goes beyond classical correlation analyses. It has been developed by Liang & Kleeman (2005), and further details are provided in Liang (2014) for the bivariable case and in Liang (2021) for the multivariate case.

The LKIF method has been compared to the PCMCI causal method and correlation in Docquier et al. (2024).

At RMI, we have applied the method to different climate problems:

• Antarctic surface mass balance (Vannitsem et al., 2019)
• Drivers of Arctic sea ice (Docquier et al., 2022; Docquier et al., 2024)
• Drivers of Antarctic sea ice (Docquier et al., 2025)
• Climate indices in the North Pacific and Atlantic regions (Vannitsem & Liang, 2022; Docquier et al., 2024; Vannitsem et al., 2025)
• Ocean-atmosphere interactions (Docquier et al., 2023).

As the original approach assumes linearity, it does not apply when the system is highly nonlinear. Pires et al. (2024) have developed an extension for the nonlinear case, which has been tested on a reduced-order atmospheric model (Vannitsem et al., 2024). Vannitsem et al. (2025) have also proposed an adaptation of the original LKIF method to cope with nonlinearities.

The figure below shows the causal graphs linking summer Antarctic sea-ice extent and its climate drivers based on the LKIF computation for 5 different CMIP6 large ensembles (Docquier et al., 2025).