What Principle Determines Climate Statistics?
A multidimensional system that is subjected to constant external forcing and dissipative processes produces permanent fluctuations. This is referred to as a dynamical equilibrium. The climate system is one example of this: It receives forcing from the Sun and produces weather. Two characteristics stand out when looking at this equilibrium state of the climate: On the one hand, there are temporal evolutions of individual weather events, which are determined by balance equations for momentum, mass, and energy. On the other hand, there is the statistical description of the weather. Although weather events appear random, statistical quantities, such as variance, which characterizes the typical strength of weather fluctuations, are well-defined for each climate variable, such as temperature. “I find it all the more surprising that the principle underlying the emergence of such climate statistics has hardly been questioned so far,” says Jin-Song von Storch from the Max Planck Institute for Meteorology. It is often implicitly assumed that the balance equations determine not only individual weather trajectories but also the statistical properties of the climate. However, this assumption falls short, as the researcher shows in a new study.
Complementary but non-reducible principles
The balance equations for momentum, mass, and energy describe individual weather trajectories by formulating local temporal tendencies. These tendencies generate incessant fluctuations. However, an effective dissipation that limits these fluctuations does not appear at the level of the time rate of change. This is because such dissipation requires interactions between the system’s components. Since these interactions only become apparent as the system evolves over time, the effective dissipation disappears at infinitely short (infinitesimal) time steps and only plays a stabilizing role over a time interval larger than zero. This is also why the effective dissipation of a climate variable generally does not correspond to the strength of the explicit damping term in the associated balance equation.
“Effective dissipation is an emergent property of the coupled system,” von Storch summarizes. “It only emerges through integration and enables the stationarity of the fluctuations, thereby making the climate statistics well-defined.”
The effective dissipation counteracts the fluctuating forcing generated by dynamics. As a result, a dynamical equilibrium emerges, along with the well-defined climate statistics that characterize this equilibrium. Jin-Song von Storch refers to the interaction between dissipation and fluctuating forcing as the “Integral Fluctuation-Dissipation Relation” (IFDR). Like the effective dissipation, the IFDR cannot be formulated as a local temporal rate of change and can therefore not be part of the classical balance equations. The equilibrium climate is thus determined by two complementary but non-reducible principles.
Possible implications of the effective dissipation
The effective dissipation acts as an internal restoring force. As such, it could influence how the climate responds to changes in the external forcing, such as an increase in greenhouse gas concentrations. Since the strength of this dissipation is related to the intensity of the fluctuations, which increase with increasing spatial model resolution, the next generation of climate models on the kilometer scale could exhibit a systematically altered climate sensitivity. This could make an important difference for climate projections.
Original publication
Jin-Song von Storch (2026): Principles of equilibrium fluctuations. Physica A: Statistical Mechanics and its Applications 683, 131218, DOI: 10.1016/j.physa.2025.131218.
Contact
Prof. Dr. Jin-Song von Storch
Max Planck Institute for Meteorology
jin-song.von.storch@mpimet.mpg.de