### Introduction

This study tries to find an answer to the question concerning the difference in obtained ellipsoidal height when the normal to the sphere is used instead of the normal to the ellipsoid. Thereby, geopotential heights (g_n = 9.80665 m/s^2) in a numerical weather model are assumed to be given at [0, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000] meters. Data were evaluated at grid points (pairs) with geodetic latitude/longitude [-90,-89,..,89,90] /[0,1,…,359,360]. The difference between two transformations, one using the normal to the ellipsoid and one using the normal w.r.t. to a mean sphere was studied.

### Submissions

GRGS volunteered to submit a solution using a radius of Re=6371009 m for the mean sphere.

- GRGS: description, data

### Results

#### RMS over each map for a given height

#### Absolute differences between heights transformed w.r.t. an normal to the ellipsoid and those transformed using a mean sphere

(Map plots can be accessed by clicking on the “o” symbols)

0 m | 10 m | 20 m | 50 m | 100 m | 200 m | 500 m | 1000 m | 2000 m | 5000 m | 10000 m | 20000 m | 50000 m | 100000 m |

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