# Vertical gradient

The change in a field or measured value in the vertical direction is referred to as a vertical gradient . With many quantities in nature, the greatest local change occurs in the perpendicular direction , so that the vertical gradient corresponds to the gradient itself.

In the geosciences , the two most important vertical gradients are the gravitational acceleration gradient and the atmospheric gradient of air temperature .

Also of greater importance are: in geophysics the vertical gradients of the magnetic field and in meteorology the vertical gradients of air pressure , water vapor ( air humidity ) and precipitation .

The hydrology partially models the vertical changes in waters and the geochemistry the gradients of chemical substances (e.g. ozone ).

## Vertical gradient of gravity

In general, the force of gravity decreases upwards, but the amount of the gradient depends on the circumstances.

### Outdoor gradient

The open-air gradient describes the change in gravitational acceleration without the presence of nearby masses that influence gravity . Assuming a completely regular, solid earth body , the theoretical open air gradient is −0.3086  mGal / m = −0.00000 3086 s −2 . The acceleration due to gravity decreases with increasing distance from the earth's surface by about 0.00031 Gal per meter of altitude . Accordingly, at a height of 1000 m above a measuring point on the earth's surface, it is 0.0031 m / s² lower than on the ground, which corresponds to a decrease of 0.031 percent per kilometer.

This value is only approximated above level ground or above a free-standing peak . In the case of uneven terrain , the topographic reduction must also be taken into account, which can achieve similar values.

### Course of gravity in the underground

Gravitational acceleration (blue) in the earth's gravity field
• In the earth's crust , the gravity gradient is around 0.11 mGal / m - the Prey gradient. However, it does not apply indefinitely in the direction of the earth's interior , because a gravity maximum occurs at a depth of approx. 1000 km, from which the force of gravity then decreases almost linearly towards the center of the earth .
• A parallel rock slab has - depending on its material - an influence of around 0.15 to 0.22 mGal per meter of slab thickness. The exact value depends on the rock density , the average of which in the earth's crust is about 2.67 g / cm³.
• This results in a Bouguer gradient of 0.1967 mGal / m - which applies exactly to the two most common rocks, granite and limestone . This vertical gradient is the standard value for the mathematical "lifting" of rock layers, which is referred to in geophysics and geodesy as gravity reduction .

## Vertical gradient of the air temperature

In general, the temperature of the earth's atmosphere decreases relatively evenly with increasing altitude up to the tropopause (10–15 km altitude):

• The mean value of the general temperature gradient is around –6 ° C per kilometer. A value of –6 K / km (sometimes –6.5 K / km) is based on the standard atmosphere , which forms the basis for calculations in meteorology and aviation . Depending on the weather, it can fluctuate a few degrees up and down. In the case of an inversion weather situation , it can be positive for a few 100 meters, i.e. H. the temperature decreases with increasing height to .

Two other vertical gradients are also important:

The differences between the three named gradients are essential for the dynamics of the weather.