Adjustment Computations, 6th Edition

CHAPTER 9ERROR PROPAGATION IN ELEVATION DETERMINATION

9.1 INTRODUCTION

Differential and trigonometric leveling are the two most commonly employed methods for determining elevation differences between stations. Both of these methods are subject to systematic and random errors. The primary systematic errors include Earth curvature, atmospheric refraction, and instrument maladjustment. The effects of these systematic errors can be minimized by following proper field procedures, or they can be modeled and corrected computationally. The random errors in differential and trigonometric leveling occur in instrument leveling, distance observations, and reading graduated scales. These must be treated according to the theory of random errors.

9.2 SYSTEMATIC ERRORS IN DIFFERENTIAL LEVELING

During the differential leveling process, sight distances are held short, and equal, to minimize the effects of systematic errors. Still, it should always be assumed that these errors are present in differential leveling observations, and thus corrective field procedures, described in this section, should be followed to minimize their effects.

9.2.1 Collimation Error

Collimation error occurs when the line of sight of an instrument is not truly horizontal and is minimized by keeping sight distances short and balanced. Figure 9.1 shows the effects of a collimation error. For an individual setup, the ...