Abstract:
Understanding the dynamics of temperature trends is crucial for accurate climate
change modelling, especially in modern times, where global environmental chal-
lenges are emerging. This study explored the application of ordinary differential
equations in climate change modelling, focusing on temperature trends. It used
Newton’s law of cooling and heating as foundational physical principles. ODEs
are powerful mathematical tools in climate science as they enable modelling of
transient and long-term temperature responses to natural and anthropogenic fac-
tors. The study developed and analyzed first-order ordinary differential equations
based on Newton’s law. dT
dt = −k(T −Ta)(0.1) where: dT
dt Rate of heat change with
respect to time, T Temperature of the object, Ta Environmental temperature, and
k Object property like the ability of the surface of an object to conduct heat. The
equations were extended and modified to accommodate complex climate systems
inherent in global and regional climate processes. The 4th-order Runge-Kutta
method was used to solve the equations in this study. Real-world data from
NASA, NOAA, and Mauna Loa sources validated the model. The model demon-
strated high accuracy in simulating local temperature trends with an average error
below 0.5°C and strong agreement between observed and simulated values. All
numerical simulations and graphical outputs were done using PYTHON software
while the results were presented using tables and graphs.
