In defense of the classical height system
Notice bibliographique
Résumé
Summary In many European countries, normal heights referred to the quasi-geoid as introduced by Molodenskij in the mid-20th century are preferred to the classical height system that consists of orthometric heights and the geoid as a reference surface for these heights. The rationale for this choice is supposed to be that in the classical height system, neither the geoid, nor the orthometric height can be ever known with centimetre level accuracy because one would need to know the topographical mass density to a level that can never be achieved. The aim of this paper is to question the validity of this rationale. The common way of assessing the congruency of a local geoid model and the orthometric heights is to compare the geoid heights with the difference between orthometric heights provided by leveling and geodetic heights provided by GNSS. On the other hand, testing the congruency of a quasi-geoidal model with normal height a similar procedure is used, except that instead of orthometric heights, normal heights are employed. For the area of Auvergne, France, which is now a more or less standard choice for precise geoid or quasi-geoid testing, only the normal heights are supplied by the Institute Geographic National, the provider of the data. This is clearly the consequence of the European preference for the Molodenskij system. The quality of the height system is to be judged by the congruency of the difference of the geoid/quasi-geoid heights subtracted from the geodetic heights and orthometric/normal heights. To assess the congruency of the classical height system, the Helmert approximation of orthometric heights is typically used as the transformation between normal and Helmert's heights is easily done. However, the evaluation of the differences between Helmert's and the rigorous orthometric heights is somewhat more involved as will be seen from the review in this paper. For the area of interest, the differences between normal and Helmert's heights at the control leveling points range between − 9.5 and 0 cm, differences between Helmert's and the rigorous orthometric heights vary between − 3.6 and 1.1 cm. The local gravimetric geoid model of Auvergne, computed by the Stokes–Helmert technique, is used here to illustrate the accuracy of the classical height system. Results show a very reasonable standard deviation (STD) of 3.2 cm of the differences between geoid values, derived from control leveling points, and gravimetric geoid heights when Helmert's heights are employed and even a smaller STD of 2.9 cm when rigorous orthometric heights are used. A corresponding comparison of a quasi-geoid model, computed by Least-Squares Modification of Stokes method, with normal heights show an STD of 3.4 cm.
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Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,001 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».