Temperature gradient

A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature spatial gradient is a vector quantity with dimension of temperature difference per unit length. The SI unit is kelvin per meter (K/m).

Temperature gradients in the atmosphere are important in the atmospheric sciences (meteorology, climatology and related fields).

Mathematical description
Assuming that the temperature T is an intensive quantity, i.e., a single-valued, continuous and differentiable function of three-dimensional space (often called a scalar field), i.e., that


 * $$T=T(x,y,z)$$

where x, y and z are the coordinates of the location of interest, then the temperature gradient is the vector quantity defined as


 * $$\nabla T = \begin{pmatrix}

{\frac{\partial T}{\partial x}}, {\frac{\partial T}{\partial y}}, {\frac{\partial T}{\partial z}} \end{pmatrix}$$

Meteorology
Differences in air temperature between different locations are critical in weather forecasting and climate. The absorption of solar light at or near the planetary surface increases the temperature gradient and may result in convection (a major process of cloud formation, often associated with precipitation). Meteorological fronts are regions where the horizontal temperature gradient may reach relatively high values, as these are boundaries between air masses with rather distinct properties.

Clearly, the temperature gradient may change substantially in time, as a result of diurnal or seasonal heating and cooling for instance. This most likely happens during an inversion. For instance, during the day the temperature at ground level may be cold while it's warmer up in the atmosphere. As the day shifts over to night the temperature might drop rapidly while at other places on the land stay warmer or cooler at the same elevation. This happens on the West Coast of the United States sometimes due to geography.

Weathering
Expansion and contraction of rock, caused by temperature changes during a wildfire, through thermal stress weathering, may result in thermal shock and subsequent structure failure.