Abstract. Earth and environmental mechanisms and phenomena are often physically finite dynamical causal processes and need more precise mathematical elaboration. Therefore this article at the beginning resumes the decomposition of general infinite circular causal relations with linear feedbacks to primary causal effects and to interactions among boundless effects and causes. In the sequel it reveals the mathematical model of general finite cause-and-effect interaction with non-linear feedback induced by finiteness of causal processes with exhaustible causal capacities. The study also uncovers that the reverse application of the mathematical model makes it possible to discover and to estimate the unknown ultimate causal capacities from relevant information of supposedly finite causal processes beyond the instant of observation. The article at the end demonstrates that the environmental relations among global climate change and ice mass losses monitored recently on Greenland and Antarctica ice sheets are plausibly finite dynamical climate processes in interaction with cryosphere.