Closing error in a level circuit

Closing error (misclosure) in a level circuit is the difference between the computed RL of the closing benchmark (or of the starting BM, if the levelling returns to it) and its known RL. It results from the accumulation of instrumental, natural and personal errors.

$$\text{Closing error} = \text{computed RL of last point} - \text{known RL of last point}$$

Permissible closing error: this depends on the class of work and the project specification, for example about $\pm 24\sqrt{K}$ mm for ordinary levelling and $\pm 12\sqrt{K}$ mm for more accurate levelling (K = length of the circuit in km). If it is exceeded, the levelling must be repeated.

Adjustment

When the error is within the limit, it is distributed among the levels of the intermediate points. The correction is proportional to the distance (or to the number of instrument setups) from the starting point:

$$\text{Correction at a point} = -\,e \times \frac{\text{distance of the point from the start}}{\text{total length of the circuit}}$$

In terms of setups: the correction at the $n$-th setup $= -\,e \times n/N$, where N is the total number of setups. The correction is applied to the CPs and BMs; each intermediate point takes the same correction as the change point just before it.

Example: computed RL of the end BM $= 100.036$ m, known RL $= 100.000$ m, 4 setups. Error $= +0.036$ m. The corrections at the CPs after the 1st, 2nd, 3rd and 4th setups are $-0.009$, $-0.018$, $-0.027$ and $-0.036$ m.