Il geoide: fusione dei dati disponibili

The geoid, i.e. the equipotential surface of the Earth's gravity field that best approximates the mean sea level, has a great importance in cartography and in environmental and civil engineering in general. In fact it allows to convert ellipsoidal heights to orthometric ones (and vice versa) and it implicitly defines the direction of the vertical at given point. Local geoid models of neighboring countries usually have different resolutions and accuracies and moreover often present inconsistencies and/or discontinuities at the borders. These anomalies are mainly due to the different height datum used in the estimation of the local geoids. However, for some engineering applications cross-border merging of multiple local geoids is necessary and cannot be based on a simple average of the two datasets in the overlapping area without taking into account the various inconsistencies and biases. To solve this problem one can take advantage of the global Earth's gravity field models estimated from satellite data: these models are not affected by local biases since they are not based on ground gravity data and therefore they may provide a correct estimate of the low frequency of the geoid undulations (wavelengths greater than 100 km). In the present work a two-step algorithm to merge local geoids using GOCE global model is presented. Firstly we estimate the biases of the two local geoids by a least squares adjustment and after that the unbiased geoids are combine by means of a collocation procedure. Particular attention is given to the estimate of the covariance function of the high frequency signal and the covariance matrix of the error of the GOCE model. After estimating a bias of about 1 m for the Italian geoid and about 0.8 m for the Swiss one, a unique Italian-Swiss "unbiased" geoid with an accuracy of few centimeters has been computed.