Weather elements like clouds, storms and rainfall are usually not isolated factors, but part of a pattern or weather system.
These weather patterns reflect fundamental forces at work in the atmosphere, including balances between winds, pressure, rotation and gravity.
Our atmosphere is a complex dynamic system in which:
Wind is crucial for many reasons.
It might seem that the wind should blow directly from high to low pressure, but it normally doesn't. This is because the Earth's rotation continuously diverts the wind to blow, more or less, along pressure-lines (isobars).
These rotational effects depend on latitude - for instance in the southern hemisphere the circulation around a low goes the 'opposite way' (clockwise).
In turn the atmospheric pressure depends on the weight of the air under gravity. The weight of a given thickness of atmosphere depends on its temperature, because warm air is less dense than cold air.
The contrast between warm and cold air masses was likened by Norwegian meteorologists of the early 20th century to a battle front. We still use their ideas of 'cold fronts' and 'warm fronts' as indicators for significant weather, but we now understand the dynamics in much more detail.
To further understand the elements and calculate our weather forecast we need to do mathematical equations.