The Structure of Climate Variability Across Scales

Abstract

One of the most intriguing facets of the climate system is that it exhibits variability across all temporal and spatial scales; pronounced examples are temperature and precipitation. The structure of this variability, however, is not arbitrary. Over certain spatial and temporal ranges, it can be described by scaling relationships in the form of power laws in probability density distributions and autocorrelation functions. These scaling relationships can be quantified by scaling exponents which measure how the variability changes across scales and how the intensity changes with frequency of occurrence. Scaling determines the relative magnitudes and persistence of natural climate fluctuations. Here, we review various scaling mechanisms and their relevance for the climate system. We show observational evidence of scaling and discuss the application of scaling properties and methods in trend detection, climate sensitivity analyses, and climate prediction.Plain Language Summary Climate variables are related over long times and large distances. This shows up as correlations for averages on long intervals or between distant areas. An important finding is that the majority of correlations in climate can be described by a simple mathematical relationship. We present such correlations for temperature on long times. Similarly, the intensity of precipitation events depends on their frequency in a simple manner. A useful concept is scaling where a scale denotes the width of an average. Scaling says that averages on different scales are related by a simple function-mathematically, this is a power law with the scaling exponent as a characteristic number. Scaling has impacts on predictability, temperature trends, and the assessment of future climate changes caused by anthropogenic forcing.

Numerical bifurcation methods applied to climate models: analysis beyond simulation

“…This first challenge I see is to better understand processes behind the background variability which is "red noise like" in Mitchell (1976) and encompasses different regimes in . Franzke et al (2019) describe the different ways (multifractal cascading processes, state-dependent noise, etc.) of how scaling behavior can appear in time series.…”

“…The "background and peaks" paradigm clearly has a problem with the explanation of the background signal and also regarding the amplitude of the variability on longer than millennial timescales (Lovejoy, 2015). On the other hand, the scaling paradigm needs a better connection to physical processes beyond the weather regime (Franzke et al, 2019). Both paradigms are also limited to temporal variability and do not address spatial patterns associated with the climate system variability.…”

Evaluation of Daily Precipitation Extremes in Reanalysis and Gridded Observation‐Based Data Sets Over Germany

“…For estimating the extremal index, we use the interval method described by Ferro and Segers (2003) where N is the number of extremes and T i is the time between the ( i + 1)th and i th extremes. The extremal index has a value range between 0 and 1, where a value of 1 indicates that the extremes occur independently from each other, while a value smaller than 1 means that they appear in clusters and there is temporal dependency, with long‐range dependence (Franzke et al., 2020) for a value of 0. See Ferro and Segers (2003) for more details.…”

Numerical Bifurcation Methods applied to Climate Models: Analysis beyond Simulation

“…This first challenge I see is to better understand processes behind the background variability which is 'red noise like' in Mitchell (1976) and encompasses all variability in ; Rypdal and Rypdal (2014). Franzke and coauthors (2019) describe the different ways (multifractal cascading processes, state-dependent noise, etc.) how scaling behavior can appear in time series.…”

“…and also regarding the amplitude of the variability on longer than millennial time scales. On the other hand, the scaling paradigm is quite abstract and lacks a clear connection to physical processes beyond the weather regime (Franzke and coauthors, 2019).…”