The course of the change in a numerical physical variable depending on the location is called a gradient or gradient (from Latin gradiens ,  striding '' ). The gradient of a size indicates for each location how much the size changes and in which direction the change is greatest.

Mathematically, the gradient is described by the vector (“direction arrow” and its length) defined by direction and magnitude , which indicates at the point under consideration in which direction the measured scalar variable increases the most and how strong the increase is; see Gradient (mathematics) .

Example: Several candles are burning in a room, spread out, on candlesticks of different heights. There is exactly one temperature gradient for each point in the room. This describes in which direction the temperature rises the most and how strong the rise is.

2. a proton gradient is the spatial or temporal difference in the concentration of protons ( e.g. acting as a pH gradient)
3. the increase or decrease in an electrochemical potential is referred to as an electrochemical gradient
4. a color gradient describes a color gradient or a transition in brightness in art and image processing
5. In road and rail construction, a gradient describes the height profile of a planned or existing route in relation to the route ( axis ).
6. The hydraulic gradient describes the groundwater gradient in hydrology (the ratio between the pressure height difference or the water level difference and the flow length).
7. In photography, the photographic density is the measure of the blackening of a light-sensitive material

The term is also used outside of physics in other disciplines to describe the course of a change in an influencing variable, for example

• as a social gradient , for the linear relationship between social status and general living conditions ( morbidity ) or life opportunities ( mortality ).
• As an ecological gradient , the gradual change of an environmental factor in an ecosystem , which is determined in a gradient analysis using gradients of factors (e.g. amount of precipitation, temperature profile) in order to document the distribution of animal or plant populations depending on these factors. A kline is a continuous change of a biological characteristic of a species in relation to an ecological gradient (e.g. a degree of latitude ).
• The goal gradient effect is the phenomenon in which a person exerts more effort to achieve a goal, the closer that person is to that goal. For this purpose, the approach gradient and avoidance gradient were also defined (see also avoidance behavior ).

The temperature gradient is a directed physical quantity that describes in the sense of a mathematical gradient at each point of a temperature field in which direction the temperature rises the most and how much . The internationally used unit  ( SI unit ) of its amount is Kelvin per meter  (K / m). The temperature gradient drives heat conduction and can cause currents (see Bénard experiment , Küppers-Lortz instability ). It plays an important role in thermophoresis and thermo-osmosis and is one of the causes of weathering . At the interfaces of substances at different temperatures, the temperature gradient - neglecting the thermal boundary layer - is not mathematically defined; vividly it goes there towards infinity .

In meteorology and geology , the vertical component of the temperature gradient is of particular interest, i.e. the change in temperature with the distance from the earth's surface. This vertical component of the temperature gradient is called the atmospheric temperature gradient in the earth's atmosphere and the geothermal depth level in the earth's crust . ${\ displaystyle {\ tfrac {\ mathrm {d} T} {\ mathrm {d} z}}}$

In temperature gradient gel electrophoresis , a process for separating charged biomolecules . For example , a temperature gradient or chemical gradient is used for DNA separation .

### meteorology

In meteorology , a gradient indicates how much a location-dependent variable changes with the location, i.e. in the horizontal or vertical direction:

There is a gradient for each point. According to the mathematical definition, a gradient has not only a magnitude , but also a direction, ie it represents a vector. This vector always points in the direction of the greatest increase in the observed variable. For example, the information on the temperature gradient in a point contains the direction of the greatest temperature difference in the vicinity of the point and the size of this difference. The component of this vector with respect to a given direction, e.g. B. the vertical, gives a directional derivative . A horizontal directional derivation of the terrain height is called a slope or a slope . The latter is also used in a figurative sense, e.g. B. Pressure gradient as the driving force of the wind (see gradient wind ).

“Hectopascal per 60 nautical miles ” (which corresponds to one degree of latitude ) was previously used as a unit for the pressure gradient  . The sense and benefit of such gradients was that tables for calculating the wind speed only had to be multiplied by the gradient factor in order to output the calculated wind speed (i.e. only tables for "Gradient = 1" were required).

## Applications

for example:

1. A pressure gradient microphone uses the pressure differences between spatial points.
2. In density gradient centrifugation, particles sediment in a density gradient .
3. In contrast to the usual nuclear magnetic resonance spectroscopy , inhomogeneous magnetic fields are deliberately used in field gradient NMR .
4. the deflection of a light beam in a material with a variable refractive index is the subject of gradient optics