Elevation

As height specify the position of the vertical distance is referred to by a reference surface in the higher geodesy. The height reference surface can be represented by a geoid, a Quasigeoid, an adapted reference ellipsoid or other geometric figure. The zero level of the reference surface was often ajar defined at a fixed mean sea level. Depending on the country or use different height and different definitions zero levels are used (see above sea level ).

• 2.1 dynamic correction
• 2.2 orthometric correction
• 2.3 normal correction
• 2.4 normal - orthometric correction

Height definitions

In general, it is expected that

The points to point ( 2) would have the same gravity potential and thus lie on an equipotential surface of the gravity: that heights are not the same geometric (1) and physically ( 2) may be correct, it can be illustrated as follows. Due to the Earth's rotation and local irregularities in the mass structure of the Earth, however, the equipotential surfaces are not parallel. Thus, the gravity due to the Earth's rotation at the poles of 1/200 is greater than at the equator, the potential energy surfaces are thus at the poles at 1/200 closer together.

There are therefore used some purely geometric or physically defined highs:

When leveling you get different height differences when you leveled along different paths. Reason for this so-called theoretical Misclosures is that the height transfer occurs along the non-parallel equipotential surfaces, the differences are but measured in meters. In order to eliminate the contradictions, a consideration of the gravity field is necessary for extensive areas with larger height differences. In practice, various metric height systems that take into account the severity, has been developed:

• Normal - orthometric or normal heights spheroidal
• Normal heights
• Orthometric heights.

There are notable differences that can achieve orders of magnitude of centimeters to tens of centimeters per kilometer in the high mountains between the height systems. The irregularities in the earth's gravitational field have been studied for about 100 years, the terms vertical deflection and gravity anomaly and geoid and now covers sufficiently accurate measurement.

Ellipsoidal heights

Geometrically defined highs are now referred to as ellipsoidal height h. These indicate the distance of a point from a geologically defined Referenzellipsoiden along the ellipsoidal. Two points of equal ellipsoidal height, however, are not on the same equipotential surface, so that water can flow between them.

Ellipsoidal heights can be determined directly by means of GPS. A simple conversion of leveled in ellipsoidal heights without knowing the severity faults is not possible. Alternatively ellipsoidal heights can be determined by applying a space polygon.

Geopotential Koten

A geopotential Kote C is the negative gravity potential difference between the point and the geoid. Points of equal geopotential Kote thus lie on an equipotential surface.

Since it is a gravity potential difference, is the SI unit joule per kilogram (J / kg ) or ( m² / s ²). To some extent, also geopotential units ( gpu ) is used as a unit (1 gpu = 10 J / kg). Previously geopotential Koten were also specified in the unit geopotential meters ( gpm). 1 gpm corresponds to 9.80665 J / kg. The amount corresponds to the dynamic height. Geopotential Koten can be determined from g leveled height differences and gravity measurements.

Or

Dynamic heights

Dynamic heights Hdyn be converted from the geopotential Koten usually with the normal gravity at sea level at 45 ° latitude in the dimension m. They express the distance that would have the equipotential surfaces at. However, the actual (metric ) distance varies by about due to the reduced acceleration of gravity at the equator towards the poles.

Dynamic heights are unusable because of the large dynamic corrections for practice. However, they result directly by a " rescaling " of the geopotential Kote.

Orthometric heights

The orthometric height H is due to the distance along the curved plumb line between a point on the earth's surface and the geoid. The geopotential Koten are translated at the average acceleration of gravity along the plumb line. The severity can not be measured inside the earth, so that they can only be calculated by setting up a hypothesis about the distribution of mass. Orthometric heights are thus subject hypothesis. Points of equal orthometric height are not on the same level surface as a rule.

The deviation between the ellipsoidal and the orthometric height is called the geoid undulation. It is globally up to 100 m, in Switzerland, for example, a maximum of 5 m.

Normal heights

Normal heights describe the distance of a point along the slightly curved normal plumb line from Quasigeoid. For the conversion of the geopotential Koten the mean normal gravity is used. The standard height is different than the orthometric height hypothesis freely determined. They were developed by the Soviet geophysicist Mikhail Sergeyevich Molodenski.

The deviation between the ellipsoidal height and the normal height is called the height anomaly or quasigeoid. In Germany this 36-50 m. Normal heights and orthometric heights vary due to deviation of the actual severity of the normal gravity. The differences can be in the high mountains up to a meter or more, in the lowlands, they are often only in the millimeter range. In the former West Germany they be -5 to 4 cm.

Normal - orthometric heights

In the absence of gravity measurements, the gravity correction of the observed differences in height can only be done with the normal gravity. The derived heights is what we call normal - orthometric heights or spheroidal - orthometric heights HSPH. The deviations from normal heights fall out small because the corrections differ only because of the small proportion of Oberflächenfreiluftgradienten.

Corrections

The actual measure of the height measurement are no elevations above sea level, but differences in height. These are usually determined in the national survey by leveling. To convert the measured height differences in a the height definitions, corrections are to be attached.

Dynamic correction

Through dynamic correction, the leveled height differences in dynamic height differences can convert.

Orthometric correction

The orthometric correction to the strictly determinable dynamic component, two hypothesis -prone location depended shares.

Assuming the average Erdkrustendichte of 2.67 g / cm ³ is true for the average severity:

Normal correction

Similarly, can be calculated using the normal correction of normal height differences. Here, the hypothesis- free mean normal heavy to be used instead of the average heavy.

Normal - orthometric correction

In the normal - orthometric correction, the normal gravity is used for dynamic correction instead of the measured gravity.

Survey

(*) The dynamic level is not the distance from the reference surface.