The hydrological cycle explains the water circulation across the earth-atmosphere interface and is fundamental in distributing the precipitation across the globe. This implies the Earth’s freshwater supplies and availability for ecosystems and living organisms, regulation of the weather patterns, estimation of the climate sensitivity and the preservation of the climate state equilibrium. Under the warming climate, the water vapour loading increases by approximately 7 % per 1 °C warming, consistent with the Clausius-Clapeyron relation. This also implies the typical climate curves shift, with the new climate state explained by the increased variance and stronger skewness leaning towards more frequent hot extremes, widening the space for long-lasting, persistent heatwaves and simultaneous severe droughts and floods in different parts of the world. The warmer climate possesses more absorbed thermal energy, primarily stored in the oceans as the main reservoirs, which regulates the heat uptake and transfer from the deep ocean to the surface, the excess latent heat release into the atmosphere, and modifies the strength of the atmospheric circulation. These factors are highly dependent on the radiative processes and jointly examined by considering the heat energy fluxes exchange by applying complex mathematical partial differential equations and multi-dimensional parametrisation schemes in the global circulation models, requiring high computational strength. Instead of solving complex mathematical equations, the philosophy is focused on investigating the energy climate budget within the simplified model, often comprising one or two dimensions, represented as the interface(s). Additionally, the simplified version breaks down the mathematical factors into summative parts, frequently producing a linearised tendency equation, encapsulating the multiple smaller-scale models within a general model. This framework allows computational flexibility and variability capture as the processes become disentangled and less reliant on each other. Hence, these models exhibit a promising starting point for understanding the planetary energy budget and conducting various climate variability and sensitivity experiments, with particular attention given to poleward heat transport and fluxes in this research.