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Global Climate Change and Its Impacts

sum of squared errors between observed data points and the fitted line, thereby determining
the optimal linear fit for the data. In climate change studies, time is used as the independent
variable, and climate variables (e.g., temperature, precipitation) as the dependent variables.
Assuming we have a series of time pointst1 ,t2 ,⋯,tnand corresponding climate variable ob-
servationsy1 ,y2 ,⋯,yn , the linear regression model can be expressed as:y=α+βt+ϵ, whereαis
the intercept;βis the slope, representing the trend of climate variables over time;ϵis the ran-
dom error term. By conducting linear regression analysis on extensive historical climate
data, we can intuitively determine whether a climate variable exhibits a long-term upward or
downward trend. For instance, linear regression analysis of global average temperature data
over the past century reveals a significant warming trend, where the slope indicates the rate
of temperature increase per unit time.
The linear regression method demonstrates significant applicability in analyzing long-
term climate change trends. It is relatively straightforward to compute, easy to understand
and interpret, and capable of quickly extracting primary trends from complex datasets. With
large volumes of dataand the trendUnder relatively stable conditions, linear regression can
provide relatively reliable results. The trend line obtained through linear regression can serve
as a fundamental reference for predicting future climate changes, offering intuitive informa-
tion for policymakers and relevant researchers. However, linear regression also has certain
limitations. Actual climate change processes are not entirely linear, as the climate system is
influenced by multiple complex factors and contains numerous fluctuations and uncertainties.
The linear regression model assumes that data changes are stationary, neglecting factors such
as seasonality, periodicity, and outliers in the data. When there are obvious nonlinear charac-
teristics or abnormal fluctuations in the data, linear regression may yield inaccurate trend es-
timates. For example, in certain regions, due to abrupt climate shifts or special geographical
environmental factors, climate data may exhibit sudden jumps or long-term nonlinear chang-
es. In such cases, linear regression results may fail to authentically reflect the actual situation
of climate change.
The moving average method is also a common tool for analyzing long-term trends in
climate change. By applying local averaging to time series data, the moving average smooths
out short-term fluctuations and highlights underlying trends. The specific implementation
involves setting a fixed-length window on the time series, calculating the average value
within the window, then sliding the window backward one time step at a time and recalcu-
lating the average value to generate a series of moving averages. Assuming the time series
data isy1 ,y2 ,⋯,yn，The window length isk，then theithsliding averageSicalculation formula
isSi=k1j=i∑i+k−1yj , wherei=1,2,⋯,n−k+1
Taking annual precipitation data as an example, when applying a 5-year moving av-
erage, we sequentially calculate the mean precipitation value for every five-year period to
obtain a new sequence. This new sequence can more clearly reveal the long-term trend of
precipitation variations while reducing interference from random annual fluctuations in pre-

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