On the spatial and temporal shift in the archetypal seasonal temperature cycle as driven by annual and semi‐annual harmonics

Abstract

Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the seasonal temperature cycle. However, an often overlooked feature of the climate seasonal cycle is the semi‐annual harmonic, which can account for a significant portion of the variance of the seasonal cycle and varies in amplitude and phase across space. Together, the spatial variation in the annual and semi‐annual harmonics can play an important role in driving processes that are tied to seasonality (e.g., ecological and agricultural processes). We propose a multivariate spatiotemporal model to quantify the spatial and temporal change in minimum and maximum temperature seasonal cycles as a function of the annual and semi‐annual harmonics. Our approach captures spatial dependence, temporal dynamics, and multivariate dependence of these harmonics through spatially and temporally varying coefficients. We apply the model to minimum and maximum temperature over North American for the years 1979–2018. Formal model inference within the Bayesian paradigm enables the identification of regions experiencing significant changes in minimum and maximum temperature seasonal cycles due to the relative effects of changes in the two harmonics.

Timescale analyses of fluctuations in coexisting populations of a native and invasive tree squirrel

“…Meteorologists and climate scientists have used harmonic analysis to document semi‐annual cycles in rainfall and temperatures whose amplitude and phase shift vary by geographical location, with moderate amplitudes for the southwest United States (Hsu & Wallace, 1976 ; White & Wallace, 1978 ). Analyzing North American temperature data from 1979 to 2018, North et al ( 2021 ) used Bayesian analysis to fit a model with annual and semi‐annual harmonics that vary over space and time. They identify geographical regions with significant changes in the contributions of the two harmonics to seasonal cycles.…”

“…In addition to a strong annual cycle, a semi‐annual cycle, which can vary by year and location, has been identified (North et al, 2021 ; White & Wallace, 1978 ). In their equation ( 1 ), North et al ( 2021 ) used the first two terms of a Fourier representation of an annual temperature time series. Their equation, using months as the time unit, is given by where x t is the temperature (in °C), t is the time (in months), a 0 is the center value for the temperature oscillations (in °C), A i is the amplitude (in °C) and ϕ i is the phase shift (in months) of the annual ( i = 1) and semi‐annual ( i = 2) component cycles.…”

“…Meteorologists and climatologists have used harmonic analysis to identify seasonal cycles in atmospheric temperature (White & Wallace, 1978 ). In addition to a strong annual cycle, a semi‐annual cycle, which can vary by year and location, has been identified (North et al, 2021 ; White & Wallace, 1978 ). In their equation ( 1 ), North et al ( 2021 ) used the first two terms of a Fourier representation of an annual temperature time series.…”

A Bayesian change point modeling approach to identify local temperature changes related to urbanization

“…There are many possible spatial and temporal basis functions to use for $$$ \mathbf{B} $$$ (e.g., Calder et al, 2002; Katzfuss & Cressie, 2012; Shen et al, 2004) and $$$ \mathbf{H} $$$ (e.g., Furgale et al, 2012; North et al, 2021; Novosad & Reader, 2016); our choice for spatial and temporal basis functions will be described in Section 4.3.…”