Nivellement Observations¶
These are measurements performed with a levelling instrument.
Levelling is a method for finding the elevation difference between points. The method is based on horizontal sight lines.
General formula for levelling:
\(H_b = H_a + (\sum H_{diff,backsight} - \sum H_{diff,foresight})\)
Levelling adjusts elevation values based on levelling observations. The adjustment is based on the same method as ordinary adjustment using least squares solution. The levelling analysis contains a statistical method and the Swedish standard for levelling.
It is fully possible to combine levelling observations with other types of observations.
The routine for selecting levelling observations must check three different situations:
- Observations between known points - do not include the observation
- Observations between a known and an unknown point - the observation is included if the unknown point is in the selection
- Observations between two unknown points - the observation is included if both unknown points are in the selection
Import of Levelling Measurements¶
When importing levelling observations, it is elevation differences between backsight and foresight, as well as distance that are imported.
We currently have the ability to retrieve data from the following formats, among others:
- Leica GSI
- Trimble DiNi (M5 format)
The options can be found under Import field book...
We can also enter observations manually. We then select New station... in the list for levelling stations.
About Network Design¶
In Gemini, it is elevation differences together with point numbers and distances that are recorded in a levelling station. In principle, we can manage with one station, but it will be much more organized with one station (levelling line) for each run between known points and junction points.
An elevation network is a traverse-like network for elevation determination (1D), where establishment typically occurs through levelling.
A levelling network is built up of one or more elevation runs as shown in the example below. The endpoints of the elevation runs are either known starting points or junction points, i.e., new points where three or more runs meet. An elevation loop is a combination of two or more elevation runs that start and end at the same known elevation point.
Legend¶
The elevation difference between elevation points, known and new, is measured through one or more instrument setups with readings forward and backward against a levelling staff. The elevation difference is measured through one or more instrument setups with a forward and backward sight.
The elevation runs get a primary measurement direction or run direction that determines the sign of the elevation difference. To be able to limit sight lengths within each elevation difference, intermediate points, unmarked transfer points (turning points), where the levelling staff is placed, are used. Equal sight lengths backward and forward in each setup should be aimed for to minimize systematic errors. The elevation runs are measured round trip, i.e., all distances are measured twice - once in each direction.
Error Equations¶
The error equation matrix for levelling observations is linear and uses the following formula:
Where:
- \(Dh\) is levelling observations
- \(v\) is corrections
- \(Z_1\) is precomputed value for point 1
- \(Z_2\) is precomputed value for point 2
- \(dz_1\) is correction for point 1
- \(dz_2\) is correction for point 2
- \((Z_2 - Z_1 - Dh)\) is the discrepancy