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
- 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 dry adiabatic gradient of -9.7 K / km, which represents the cooling of a rapidly rising dry air parcel. However, it changes in the presence of water vapor
- Moist adiabatic gradient , which is around -5 K / km from the dew point (with cloud or fog formation).
The differences between the three named gradients are essential for the dynamics of the weather.