Assessment of GOCE Models Over Mexico and Canada and Impact of Omission Errors

Abstract

This paper reports a series of comparisons of geoidal heights derived from several GOCE models with (1) geoidal heights derived from GPS on benchmarks (referred to as geometric geoidal heights) over Mexico and Canada, and with (2) geoidal heights derived from the latest geoidal maps of Mexico (GGM2010) and Canada (PCGG2013) (referred to as gravimetric geoidal heights). The paper also looks quantitatively into omission errors. Comparison (1) and (2) were carried out not including and including omission errors. The GOCE models used in comparison (1) disregarding omission errors are the direct solution model (first, second and third generations), the time-wise solution model (first, second and third generations), GOCO02S model and GIF48 model, all evaluated up to their maximum degree/order. Only GOCE direct third generation model was used in comparison (1) considering omission errors, and in comparison (2) disregarding omission errors, the latter with respect to GGM2010. The GOCE models used in comparison (2) including correction for omission errors are the GOCE direct third generation, GOCO01S, GOCO03S and DGM-1S models, evaluated up to degree/order 180. This makes GOCE direct third generation as the only model common in all comparisons. Omission errors were evaluated based on the extra-high degree harmonics of EGM2008. The omission errors in Mexico and in Canada show a similar behaviour, with a near zero mean and a standard deviation at the order of ±50 cm in Mexico and ±45 cm in Canada. In both cases, maximum differences reach more than 4 m. The effect of omission errors can be better appreciated by looking at performance of the only GOCE model used in all comparisons, the direct third generation model. Comparing it with Mexican geometric geoidal heights: without correcting for omission errors, mean and standard deviation of −5.1 and ±45.7 cm; including correction for omission errors, mean and standard deviation of −1.6 ± 30.6 cm. Comparing it with GGM2010: without correcting for omission errors, mean and standard deviation of −17.4 and ±51.3 cm; including correction for omission errors, mean and standard deviation of −2.8 ± 34.8 cm.