<p>To understand the plethora of important processes that are characterized by their complexity, from global pandemics to global climate change, it may be critical to quantify causal contributions between time series variables. Here, we examine an empirical linear relationship between the rate of changing causes and effects with various multipliers. Sign corrected normalized information flow (<em>nIF<sub>c</sub></em>) tends to provide the best estimates of causal contributions, often in situations where such causality is poorly reflected by regressions. These include: i) causal contributions with alternating feedback (correlation) sign, ii) significant causal time-lags, iii) significant noise contributions, and iv) comparison among many causes to an overall mean effect, especially with teleconnection. Estimates of methane-climate feedbacks with both observational and Earth system model CESM2 data are given as examples of nonlinear process quantification and model assessment. The relative causal contribution is hypothesized to be proportional to |<em>nIF</em>|, i.e. the ratio between entropy (degree of uncertainty) received from the cause-variable (i.e. information flow, |<em>IF</em>|) and the total entropy change of the effect-variable. Large entropy, associated with noise, deteriorates the estimates of total entropy change, and hence <em>nIF</em>, while the proportional relationship between the relative causal contribution and <em>IF</em> improves.</p>