TITLE:
Variable Daily Air Temperature Model for Analysis and Design
AUTHORS:
G. Danko, C. Lu
KEYWORDS:
Air Temperature Model, Deterministic and Stochastic Changes, Temperature Trends
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.8,
August
30,
2018
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.