Correction

This article refers to:

Using AUSGeoid2020 and its error grids in surveying computations

Article title: Using AUSGeoid2020 and its error grids in surveying computations

Author: W. E. Featherstone, J. C. McCubbine, S. J. Claessens, D. Belton, and N. J. Brown

Journal: Journal of Spatial Science

DOI: 10.1080/14498596.2018.1559774

When the above article was first published online, equation (9)(9) $z=Z+\left(\xi \mathit{.}cos\left(\alpha \right)\mathit{+}\eta \mathit{.}sin\left(\alpha \right)\right)$(9) on page 369 contains a sign error, so should read (addition instead of subtraction):

(9) $z=Z+\left(\xi \mathit{.}cos\left(\alpha \right)\mathit{+}\eta \mathit{.}sin\left(\alpha \right)\right)$(9)

This affects the numerical values in Tables 3 and 4; the corrected Tables are provided below. This sign error does not affect Eq. (10), which remains correct. This sign error was discovered by Nic Gowans (NSW Spatial Services) based on the residuals of his least squares adjustments, and we thank him for bringing this error to our attention. The surveyor’s worst nightmare: “a rogue sign”! Our apologies …

Table 3. Worked examples of reducing measured zenith angles to geodetic zenith angles (Eq. 9)(9) $z=Z+\left(\xi \mathit{.}cos\left(\alpha \right)\mathit{+}\eta \mathit{.}sin\left(\alpha \right)\right)$(9) and error propagation (Eq. 10) using the deflection errors from Appendix A. The [unrealistic] cases of zero observational error are included to assist in gauging the relative contributions of the deflection errors.

Measured zenith angle ($Z$)	Uncertainty $\sigma (Z)$	Geodetic azimuth of line ($\alpha$)	Uncertainty $\sigma (\alpha )$	Geodetic zenith angle ($z$)	Uncertainty $\sigma (z)$
45° 00’ 00”	±2”	00° 00’ 00”	±1”	45° 00’ 02.44”	±3.48”
85° 00’ 00”	±2”	45° 00’ 00”	±1”	84° 59’ 56.10”	±3.59”
89° 00’ 00”	±2”	90° 00’ 00”	±1”	88° 59’ 52.04”	±3.70”
45° 00’ 00”	±0”	00° 00’ 00”	±0”	45° 00’ 02.44”	±2.85”
85° 00’ 00”	±0”	45° 00’ 00”	±0”	84° 59’ 56.10”	±2.98”
89° 00’ 00”	±0”	90° 00’ 00”	±0”	88° 59’ 52.04”	±3.11”

Table 4. Worked examples of reducing measured directions to the ellipsoid (Eq. 11) and error propagation (Eq. 12) using the deflection errors from Appendix A. The [unrealistic] cases of zero observational error are included to assist in gauging the relative contributions of the deflection errors.

Measured horizontal direction ($D$)	Uncertainty $\sigma (D)$	Geodetic zenith angle ($z$)	Uncertainty $\sigma (z)$	Geodetic azimuth of line ($\alpha$)	Uncertainty $\sigma (\alpha )$	Reduced horizontal direction ($d$)	Uncertainty $\sigma (d)$
45° 00’ 00.00”	±1”	45° 00’ 02.44”	±3.48”	45°	±1”	44° 59’ 52.65”	±3.15”
45° 00’ 00.00”	±1”	84° 59’ 56.10”	±3.59”	45°	±1”	44° 59’ 59.36”	±1.03„
45° 00’ 00.00”	±1”	88° 59’ 52.04”	±3.70”	45°	±1”	44° 59’ 59.87”	±1.00”
45° 00’ 00.00”	±0”	45° 00’ 02.44”	±0”	45°	±0”	44° 59’ 52.65”	±2.98”
45° 00’ 00.00”	±0”	84° 59’ 56.10”	±0”	45°	±0”	44° 59’ 59.36”	±0.26”
45° 00’ 00.00”	±0”	88° 59’ 52.04”	±0”	45°	±0”	44° 59’ 59.87”	±0.05”

The online version of this article has been corrected.