4.1.3. Non-stationarity

Statistical analysis of the difference between mean CO2 concentration (ppm) in the 1980s and mean CO2 concentration in the 2000s, captured by Mauna Loa, Hawaii, which has the longest continuous record of direct atmospheric CO2 measurements, showed that there has been a significant change in mean maximum temperature from decade to decade, and established that there is statistical evidence to claim that climate variables are changing over time.

This statement introduces the concept of non-stationarity by highlighting how it is evident in changes in atmospheric CO2 concentrations as measured over the decades. By comparing CO2 levels from the 1980s to the 2000s, researchers observe clear trends in temperature changes, indicating that our climate is not consistent over time. This inconsistency, termed 'non-stationarity,' signifies that climate patterns are evolving rather than remaining fixed.

Imagine a garden where the types of flowers planted change from season to season, moving from roses to daisies as the temperature and weather change. Just like the flowers adapting to their environment, climate variables like CO2 levels and temperatures are constantly changing over the years, indicating non-stationarity.

The climate system is constantly changing across time, and these changes are usually associated with the temporal (time related) variation of the statistical properties of climatic variables, such as temperature, precipitation, wind speed, relative humidity, volcanic activity, seasonal change, and solar radiation levels.

This chunk elaborates on the concept of climate system changes, explaining that different climate factors fluctuate over time. This includes variables like temperature and precipitation that define our weather and climate conditions. When these variables change in their patterns or averages, it indicates non-stationarity, as the climate is always in flux rather than remaining stable.

Think of a music playlist. If a playlist stays the same, it’s like a stationary climate—boring and predictable. But if you keep switching songs based on the mood or season (like upbeat songs in summer and mellow songs in winter), that’s like a non-stationary climate where conditions are continually changing.

Statistically, it poses non-stationarity, i.e., the status of a time series whose statistical properties are changing through time, and is opposite of a stationary time series which has statistical properties or moments (e.g., mean and variance) that do not vary in time.

This section defines non-stationarity in statistical terms, contrasting it with stationarity. A stationary time series has properties like mean and variance that remain constant over time. In contrast, non-stationarity implies that the average values and fluctuations of climate variables evolve, indicating a more complex understanding of climate dynamics.

Imagine a basketball player. If he always scores the same number of points in every game, that's like a stationary time series; it's predictable. However, if his score changes game by game—sometimes he scores high, sometimes low—that's like a non-stationary series where the outcome varies.

Beuno de Mesquita, et al. (2020) define non-stationarity as 'a change in the relationship, either in direction or magnitude (from a significant relationship to no relationship and vice versa) between variables over time.' They further add that 'such non-stationarity is often combined with the additional hurdle of needing multivariate statistics.'

This statement offers insights into how relationships between different climate variables can change over time, reflecting the intricate nature of climate interactions. Non-stationarity can complicate data analysis because it may alter expected relationships between factors like temperature and precipitation, indicating that previous correlations may no longer hold true. This requires advanced statistical methods to properly analyze.

Imagine two friends whose friendship fluctuates over time; sometimes they get along great, other times they have conflicts. As their relationship changes, predicting future interactions becomes challenging. Similarly, in climate studies, changes in relationships between variables like temperature and rainfall can make understanding and predicting climate patterns more difficult.

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