Refinamento do modelo geoidal brasileiro e criação do modelo de anomalia de altura por meio de geoestatística para a cidade de Itaqui/RS

Abstract

The present work implemented a methodology for the refinement of the Brazilian geoidal model, MapGeo2015 and creation of a model of height anomaly. For the initial construction of the geoidal model and anomaly, it was necessary to calculate the point values of the geoid undulation (N), subtracting the ellipsoidal altitude (h) from the orthometric (H) and normal altitude (HN). From these values were made two correction models applied to the true ripple values extracted from the Brazilian geoidal model. From the generated models, a grid with 103 vertices was created, and the National Grid Reference Networks (RRNN), located in the urban perimeter of Itaqui / RS, were used as control points. The RN 1931A, located in Praça Marechal Deodoro, was used the RN 1923X located in E.E. of Fundamental Education Aníbal Loureira and RN1931B of E.E. Tito Côrrea Lopes. The geometric equation (H) and normal (HN) elevation values of the High Accuracy Altimetric Network (RAAP) of the Brazilian Geodetic System (SGB) were refined by means of geostatistics, Minimum Square Method (MMQ) and of Equation of Condition or Correlates. Two correction models were created, the first one was based on the difference between the values of MapGeo2015 and absolute geoid ripple, originating the Geoidal Correctional Model (MCG), the second was in an equivalent way, however replacing the geoid undulation by the anomaly height and orthometric altitude by normal altitude, shaping the Correctional Anomaly Model (MCA). After geostatistical procedures, the values of height and geoidal undulation were determined for the vertices that served as a benchmark test for both models. The values of the MCA and MCG models were extracted and subtracted from the calculated values of orthometric altitude and normal altitude, obtaining the arithmetic mean (𝑋̅) for the orthometric (H*) altitude of 0.0013 m and for normal altitude (HN*) of -0.0012 m. These values dismantle the quality obtained in the execution of the geometric leveling, being qualified within the class IN with errors less than 12 mm √𝑘, according to NBR 13.133. The standard deviation of the calibration test vertices for orthometric and normal altitudes was calculated, resulting in 0.0224 m and 0.0222 m, centimetric values that served as parameters in the applicability of the correction models of height anomaly and geoidal undulation for the MapGeo2015. Both results limited the use of the applicability of the correctional models in geodesic works, in the order of millimeters. However, the essence of the work that was the creation of two correctional models, one of height anomaly and another of geoidal undulation for the MapGeo2015, remained partially in full, so it is possible to extract values of orthometric and normal altitudes within of the vertex mesh by means of geodetic scans in the centimeter house.