Abstract
An analytical model, TA(t), for the observed outside air temperature change, Ta(t), with time is developed using two components: one for the variation caused by the Earth’s movement, plus any other quasi-stationary thermodynamic effects due to industrialization; and one for the random variation caused by stochastic and/or chaotic, local environmental changes. The first component, TR(t), describes a regular trend, expressed by periodic functions of time and constants unchanged with time. The second component, TS, is a random, stochastic variation. For the observed outside air temperature, the analytical model of TA(t)=TR(t) +TS is such as to give a statistically best approximation for the observed time period with = min. Several versions for the TR(t) functions are defined and tested in the study for an example location for 20 years. The best model for TR(t) t is found as a linear function with time plus a variable-coefficient Fourier series with linearly changing amplitude with time. It is found that the final analytical temperature, TA(t), can be used not only to represent the historical daily mean temperature but also to predict the future daily mean temperature at the given location. The upper and lower boundaries give safety limits for the temperature prediction. The stochastic component identified in the model is stable and stationary. The method of model identification for TA(t) can be used for determining input temperature functions for supporting engineering design; or for an unbiased scientific inquiry of temperature change with time in climate studies.
Highlights
Climate is one of the main elements of the natural environment
TA (t ), for the observed outside air temperature change, Ta (t ), with time is developed using two components: one for the variation caused by the Earth’s movement, plus any other quasi-stationary thermodynamic effects due to industrialization; and one for the random variation caused by stochastic and/or chaotic, local environmental changes
Common expectation dictates that the linear regression evaluation for the 20-year long time period of the original data may provide an un-biased result for the linear change in the magnitude of Ta (t )
Summary
Temperature has a direct impact on atmospheric stability, evaporation, precipitation, and many other conditions of life [1]. The daily maximum temperatures have increased more rapidly than the decrease in the low temperatures in the last century resulting in a risen mean temperature of about 1.6 ̊C [3]. An extrapolation for the century would give an increase about 3 ̊C to 5 ̊C in the global mean annual temperature [4]. A more exact forward prediction approach may give different result. It is difficult, to analyze slowly-changing trends in the outside temperature as they are buried within large-amplitude, harmonic, cyclic variations as well as stochastic and/or chaotic changes
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