If heat flows to the Earth's surface from both the Sun and the Earth's interior, why do we say that the motions of the atmosphere are powered by the Sun?

Understanding the Earth's heat sources is essential in grasping why our planet functions as it does. The Earth is primarily heated by two sources; the Sun, which delivers a constant stream of solar radiation, and the Earth's own interior, which radiates residual heat from the planet's formation and from radioactive decay. While the Sun's energy is powerful enough to initiate major atmospheric dynamics by heating the planet's surface, the heat emanating from the Earth's core primarily affects geological processes such as the movement of tectonic plates and volcanic activity. It's the interplay of these heat sources that shapes our environment, but for atmospheric motions, the Sun is the dominant player.

The dance of the atmosphere is a complex, continual performance driven by the Sun's energy. As solar radiation reaches the Earth, it warms the surface unevenly due to factors like angle of incidence, varied surface albedo, and different land or water masses. This uneven heating results in a variety of temperature zones, which in turn cause variations in pressure. Higher temperatures lead to lower pressure, and cooler temperatures result in higher pressure. These temperature and pressure differentials push and pull air masses around in the vast atmospheric circulation system, creating everything from gentle breezes to powerful storms.

Temperature and pressure gradients are fundamental to understanding weather and climate. A gradient is simply a way of expressing a difference in temperature or pressure over a distance. In terms of the atmosphere, these gradients drive air movement, as air naturally flows from areas of high pressure to areas of low pressure. The greater the difference, the stronger the winds. Gradients are also influenced by the Earth's rotation, which introduces Coriolis forces, adding to the complexity of atmospheric motion and leading to the formation of distinct weather systems.

Solar energy and geothermal energy are two vastly different players when it comes to influencing Earth's atmosphere. The Sun's solar energy is the powerhouse of climate and weather. It heats the surface, generating temperature differentials that drive atmospheric circulation. Geothermal energy, on the other hand, is the Earth's internal heat. Despite its importance in geological formations and maintaining the planet’s core temperature, it contributes negligibly to atmospheric dynamics. This is due to its minimal intensity compared to the vast power of solar energy reaching the Earth's surface.

The interaction between the Earth's surface and the atmosphere underlies the formation of weather patterns and climatic systems. Whether it's the daily weather that fluctuates or the long-term climatic trends, these conditions are governed by heat exchange and the resulting atmospheric movements. Climate systems, like the El Niño Southern Oscillation, are larger-scale examples of how solar-heated water and air circulations can impact global weather patterns. In contrast, weather events, like localized thunderstorms, illustrate the immediate and dynamic reaction of the atmosphere to the Sun's influence via temperature and pressure changes. It's the Sun's reliable output of energy that powers the complex, diverse, and ever-changing weather and climate on our planet.