{{unreferenced, date=July 2016
A spatial gradient is a
gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...
vector norm
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is ze ...
equal to zero.
When evaluated over
vertical position
Vertical position or vertical location, also known as vertical level or simply level, is a position along a vertical direction above or below a given vertical datum (reference level).
Vertical distance or vertical separation is the distance betw ...
(altitude or depth), it is called vertical gradient.
Examples:
;Biology
* Concentration gradient, the ratio of solute concentration between two adjoining regions
*
Potential gradient
In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because i ...
, the difference in electric charge between two adjoining regions
;Fluid dynamics and earth science
*
Density gradient Density gradient is a spatial variation in density over an area. The term is used in the natural sciences to describe varying density of matter, but can apply to any quantity whose density can be measured.
Aerodynamics
In the study of supersonic ...
*
Pressure gradient
In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The p ...
Geothermal gradient
Geothermal gradient is the rate of temperature change with respect to increasing depth in Earth's interior. As a general rule, the crust temperature rises with depth due to the heat flow from the much hotter mantle; away from tectonic plate bo ...
**
Sound speed gradient In acoustics, the sound speed gradient is the rate of change of the speed of sound with distance, for example with depth in the ocean,
or height in the Earth's atmosphere. A sound speed gradient leads to refraction of sound wavefronts in the direct ...
*
Wind gradient
In common usage, wind gradient, more specifically wind speed gradient
or wind velocity gradient,
or alternatively shear wind,
is the vertical component of the gradient of the mean horizontal wind speed in the lower atmosphere. It is the rate of ...
Grade (slope)
The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero in ...
*
Time derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t.
Notation
A variety of notations are used to denote th ...
*
Material derivative
In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material der ...
*
Structure tensor
In mathematics, the structure tensor, also referred to as the second-moment matrix, is a matrix derived from the gradient of a function. It describes the distribution of the gradient in a specified neighborhood around a point and makes the inf ...