{"id":26187,"date":"2021-10-19T19:15:15","date_gmt":"2021-10-19T19:15:15","guid":{"rendered":"https:\/\/adenilsongiovanini.com.br\/blog\/?p=26187"},"modified":"2023-03-03T01:02:39","modified_gmt":"2023-03-03T01:02:39","slug":"modelo-geoidal-o-que-e-e-qual-o-oficial-do-brasil","status":"publish","type":"post","link":"https:\/\/adenilsongiovanini.com.br\/blog\/modelo-geoidal-o-que-e-e-qual-o-oficial-do-brasil\/","title":{"rendered":"Modelo Geoidal?"},"content":{"rendered":"<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><strong>Modelo geoidal<\/strong>, voc\u00ea acabou de encontrar um artigo definitivo sobre o tema:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Com a leitura do mesmo voc\u00ea aprender\u00e1:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O que \u00e9 um <strong>modelo geoidal<\/strong>;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O que \u00e9 o <strong>Geoide<\/strong>;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Qual o conceito de <strong>Elipsoide<\/strong>;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Qual a diferen\u00e7a entre <strong>altitude ortom\u00e9trica<\/strong> e <strong>altitude geom\u00e9trica <\/strong><\/span><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">e;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Quais os modelos geoidais utilizados no Brasil.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Prossiga a leitura com m\u00e1xima aten\u00e7\u00e3o.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O que \u00e9 um modelo geoidal<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">De acordo com o <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ibge.gov.br\/\">IBGE<\/a><\/span> um <strong>modelo geoidal<\/strong> \u00e9:<\/span><\/p>\n<blockquote style=\"border: 2px double #009900; background: #f0fff0 none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: #323232; padding-left: 15px; padding-top: 10px; padding-bottom: 10px;\">\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Um modelo digital que fornece os fatores para convers\u00e3o das altitudes dadas pelos <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/receptor-gnss-quando-utilizar\/\">receptores GNSS<\/a><\/span>, resultando em altitudes compat\u00edveis com a gravidade terrestre, mais adequadas para descrever o escoamento de massas l\u00edquidas, como as necess\u00e1rias em grandes projetos de irriga\u00e7\u00e3o, gera\u00e7\u00e3o hidrel\u00e9trica etc.<\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Em termos t\u00e9cnicos, um modelo para convers\u00e3o de <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/altitude-ortometrica\/\" style=\"color: #0000ff;\">altitudes<\/a><\/span> descreve numericamente a separa\u00e7\u00e3o entre o elipsoide de refer\u00eancia das altitudes geom\u00e9tricas \u2013 tamb\u00e9m chamadas elipsoidais, resultantes da utiliza\u00e7\u00e3o dos <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/operador-de-gnss\/\" style=\"color: #0000ff;\">Sistemas Globais de Navega\u00e7\u00e3o por Sat\u00e9lites (GNSS)<\/a><\/span> \u2013 e a superf\u00edcie de refer\u00eancia das altitudes f\u00edsicas, isto \u00e9, no caso do Brasil, o<span style=\"color: #0000ff;\"> <a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/datum-vertical-o-que-e-e-qual-o-do-brasil\/\" style=\"color: #0000ff;\">datum vertical<\/a><\/span> da Rede Altim\u00e9trica de Alta Precis\u00e3o (RAAP) do <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/sistema-geodesico-brasileiro-o-que-e\/\" style=\"color: #0000ff;\">Sistema Geod\u00e9sico Brasileiro<\/a><\/span> (SGB). A partir das <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/coordenadas-geodesicas-o-que-sao\/\" style=\"color: #0000ff;\">coordenadas geod\u00e9sicas<\/a><\/span> resultantes do adequado processamento das observa\u00e7\u00f5es coletadas por meio de um receptor GNSS geod\u00e9sico, deve-se extrair do modelo o fator para convers\u00e3o da altitude geom\u00e9trica em altitude f\u00edsica.<\/span><\/p>\n<\/blockquote>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Para entendermos melhor o que \u00e9 um modelo geoidal, precisamos entender o que s\u00e3o:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">O geoide;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">O elipsoide;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Um datum;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">A altitude ortom\u00e9trica e;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">A altitude elipsoidal.<\/span><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">Modelo geoidal &#8211; O que \u00e9 o geoide?<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px;\"><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O <strong>geoide<\/strong> \u00e9 a <strong>figura matem\u00e1tica que mais se aproxima a forma real do planeta<\/strong>.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O mesmo pode ser conceituado como:<\/span><\/p>\n<blockquote style=\"border: 2px double #009900; background: #f0fff0 none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: #323232; padding-left: 15px; padding-top: 10px; padding-bottom: 10px;\"><p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O n\u00edvel m\u00e9dio dos mares suposto em equil\u00edbrio, prolongado ao longo dos continentes e sobre a influ\u00eancia da for\u00e7a da gravidade e da massa da terra.<\/span><\/span><\/p><\/blockquote>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Este prolongamento do n\u00edvel m\u00e9dio dos mares possibilita a cria\u00e7\u00e3o de uma superf\u00edcie fict\u00edcia <\/span><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">equipotencial gravitacional, o que significa que todos os seus pontos superficiais possuem a mesma for\u00e7a da gravidade.<\/span><\/p>\n<p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O <strong>geoide<\/strong> f<\/span><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">oi introduzido em 1828 por <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" title=\"Carl Friedrich Gauss\" href=\"https:\/\/pt.wikipedia.org\/wiki\/Carl_Friedrich_Gauss\">Carl Friedrich Gauss<\/a><\/span>, por\u00e9m recebeu este nome somente em 1873 por J. F. Listing. <\/span><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A precis\u00e3o que encontramos atualmente, no entanto, s\u00f3 foi alcan\u00e7ada nos anos 1990, com a Solu\u00e7\u00e3o Precisa do Geoide, de <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/en.wikipedia.org\/wiki\/Petr_Van%C3%AD%C4%8Dek\" target=\"_blank\" rel=\"noopener noreferrer\">Petr Van\u00ed\u010dek<\/a><\/span> e sua equipe, que permite que se tenha uma exatid\u00e3o de cent\u00edmetros a mil\u00edmetros na computa\u00e7\u00e3o geoidal. <\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">De acordo com Carl Friedrich Gauss, o geoide \u00e9 a &#8220;figura f\u00edsica da Terra&#8221; que, em m\u00e9dia, coincide com o valor m\u00e9dio do n\u00edvel m\u00e9dio das \u00e1guas do mar.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Por causa desta caracter\u00edstica, a <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"http:\/\/adenilsongiovanini.com.br\/blog\/altitude-ortometrica\/\" target=\"_blank\" rel=\"noopener noreferrer\">altitude ortom\u00e9trica<\/a><\/span> (altitude em rela\u00e7\u00e3o ao modelo geoidal) \u00e9 a <strong>altitude utilizada em obras de engenharia<\/strong>.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Na realidade, embora seja utilizado para aproximar a forma do planeta, o <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/geoide\/\">geoide<\/a><\/span> \u00e9 consideravelmente mais suave do que a superf\u00edcie f\u00edsica terrestre. <\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Enquanto que a superf\u00edcie terrestre varia entre os +8850 m (Monte Everest) e \u221211000 m (Fossa das Marianas), o geoide varia apenas em cerca de \u00b1100 m.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">Modelo geoidal &#8211; O que \u00e9 o elipsoide?<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3666\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide.png\" alt=\"modelo geoidal - conceito de elipsoide\" width=\"503\" height=\"426\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide.png 503w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/11\/elipsoide-300x254.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O <strong>elipsoide<\/strong> \u00e9 uma figura matem\u00e1tica mais simples do que o geoide. Isso porque o mesmo possui apenas 2 par\u00e2metros. S\u00e3o eles:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Semi-eixo maior e;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"> o semi-eixo menor.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">O mesmo precisou ser criado, pois o geoide era demasiadamente complexo para ser utilizado no dia a <\/span><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">dia.<\/span><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A<\/span><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"> <em><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.todamateria.com.br\/altitude\/\">altitude<\/a><\/span> obtida em rela\u00e7\u00e3o ao <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/elipsoide-de-revolucao-o-que-e\/\">elipsoide<\/a><\/span><\/em> \u00e9 a <strong>altitude geom\u00e9trica<\/strong>.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Como que o elipsoide, o geoide e a superf\u00edcie topogr\u00e1fica s\u00e3o amarrados?<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3939\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum.png\" alt=\"altitude ortom\u00e9trica o que \u00e9 um datum\" width=\"679\" height=\"385\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum.png 679w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/datum-300x170.png 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O elipsoide, o geoide e a superf\u00edcie topogr\u00e1fica s\u00e3o amarrados atrav\u00e9s de um <strong>datum<\/strong> (tamb\u00e9m conhecido como superf\u00edcie de refer\u00eancia), sendo que um datum possui 3 par\u00e2metros. S\u00e3o eles:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um ponto de amarra\u00e7\u00e3o;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um elipsoide e;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Um norte.<\/span><\/li>\n<\/ul>\n<p>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Com isso, ao utilizar um software de Geoprocessamento voc\u00ea n\u00e3o est\u00e1 utilizando um elipsoide e sim um <span style=\"color: #0000ff;\"><a href=\"http:\/\/adenilsongiovanini.com.br\/blog\/datum-o-que-e-e-para-que-serve\/\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"color: #0000ff;\">datum<\/a><\/span>. O elipsoide \u00e9 somente um dos elementos que constituem o datum.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Qual a diferen\u00e7a entre altitude ortom\u00e9trica e altitude geom\u00e9trica<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3977\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/altitude-ortom\u00e9trica-e-altitude-geom\u00e9trica.png\" alt=\"altitude ortom\u00e9trica e altitude geom\u00e9trica\" width=\"755\" height=\"336\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/altitude-ortom\u00e9trica-e-altitude-geom\u00e9trica.png 755w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/altitude-ortom\u00e9trica-e-altitude-geom\u00e9trica-300x134.png 300w\" sizes=\"(max-width: 755px) 100vw, 755px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A <strong>altitude geom\u00e9trica<\/strong>, tamb\u00e9m conhecida como altitude elipsoidal \u00e9 a <em>altitude em rela\u00e7\u00e3o ao <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/elipsoide-o-que-e-e-para-que-serve\/\">elipsoide<\/a><\/span><\/em>. A mesma \u00e9 a altitude obtida com um receptor GNSS.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">J\u00e1 a altitude ortom\u00e9trica \u00e9 a altitude em rela\u00e7\u00e3o ao geoide, sendo que a mesma \u00e9 que deve ser utilizada em obras de engenharia. <\/span><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px;\"><strong><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Entendendo o modelo geoidal<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O modelo geoidal, tamb\u00e9m conhecido como ondula\u00e7\u00e3o geoidal descreve a separa\u00e7\u00e3o entre o geoide e o elipsoide.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Na imagem abaixo existente na contracapa da <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"http:\/\/www.carto.eng.uerj.br\/cdecart\/download\/NBR14166.pdf\">NBR 14.166<\/a><\/span> a <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/modelo-de-ondulacao-geoidal\/\" target=\"_blank\" rel=\"noopener noreferrer\">ondula\u00e7\u00e3o geoidal<\/a><\/span> aparece destacada com a letra N.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter wp-image-3978 size-large\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ondula\u00e7\u00e3o-geoidal-780x554.png\" alt=\"modelo geoidal\" width=\"780\" height=\"554\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ondula\u00e7\u00e3o-geoidal-780x554.png 780w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ondula\u00e7\u00e3o-geoidal-300x213.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ondula\u00e7\u00e3o-geoidal-768x546.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/Ondula\u00e7\u00e3o-geoidal.png 992w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Perceba que n\u00f3s temos o elipsoide e o geoide. <\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Perceba tamb\u00e9m que a letra &#8220;h&#8221; representa a <strong>altitude em rela\u00e7\u00e3o ao elipsoide<\/strong> (altitude elipsoidal ou geom\u00e9trica), que \u00e9 a altitude obtida com receptores GNSS.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">J\u00e1 a letra &#8220;H&#8221;, representa a altitude em rela\u00e7\u00e3o ao geoide (altitude ortom\u00e9trica), que \u00e9 a altitude que deve ser utilizada em obras de engenharia.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O <strong>modelo geoidal<\/strong> (tamb\u00e9m conhecido como ondula\u00e7\u00e3o geoidal) \u00e9 o modelo que serve de base para a transforma\u00e7\u00e3o da altitude de elipsoidal para ortom\u00e9trica.<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A f\u00f3rmula que possibilita este c\u00e1lculo \u00e9:<\/span><\/p>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">N=h-H <\/span><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Onde:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">N= <span style=\"color: #0000ff;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/blog\/ondulacao-geoidal-o-que-e-e-como-calcular\/\" style=\"color: #0000ff;\">Ondula\u00e7\u00e3o geoidal<\/a><\/span>;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">H = Altitude ortom\u00e9trica e;<\/span><\/li>\n<li><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\">h= <span style=\"color: #0000ff;\">Altitude geom\u00e9trica<\/span>.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">V\u00eddeo a respeito do assunto.<\/span><\/p>\n<p><center><iframe width=\"728\" height=\"410\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/CB9N7-YNz24\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/center><\/p>\n<p>&nbsp;<\/p>\n<h3 lang=\"en-CA\" style=\"text-align: center;\" align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><strong>Que dados s\u00e3o utilizados para a atualiza\u00e7\u00e3o do modelo geoidal<\/strong><\/span><\/h3>\n<p><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3889\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/dados-gravim%C3%A9tricos.jpg\" alt=\"geoide - dados gravim\u00e9tricos\" width=\"708\" height=\"732\" \/><\/span><br \/>\n<span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A atualiza\u00e7\u00e3o do <strong>modelo geoidal<\/strong> \u00e9 feita atrav\u00e9s da utiliza\u00e7\u00e3o de <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"http:\/\/dados.gov.br\/dataset\/cged_bdg_eg\" target=\"_blank\" rel=\"noopener noreferrer\">dados gravim\u00e9tricos<\/a><\/span> coletados no territ\u00f3rio brasileiro e de novos modelos globais do geopotencial. Tamb\u00e9m se faz a utiliza\u00e7\u00e3o do aprimoramento das t\u00e9cnicas utilizadas nos c\u00e1lculos.<\/span><\/p>\n<p lang=\"en-CA\" align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">No caso, todas as atualiza\u00e7\u00f5es s\u00e3o feitas pelo <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ibge.gov.br\/\">IBGE<\/a><\/span> juntamente com a <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.poli.usp.br\/\">Escola Polit\u00e9cnica da Universidade de S\u00e3o Paulo<\/a><\/span>.<\/span><\/p>\n<p lang=\"en-CA\" align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">O resultado destas atualiza\u00e7\u00f5es \u00e9 uma aplica\u00e7\u00e3o desktop para ambiente Windows denominada <strong>MAPGEO<\/strong>, que possibilita a interpola\u00e7\u00e3o dos valores da ondula\u00e7\u00e3o geoidal a partir da grade regular que representa o modelo.<\/span><\/p>\n<p lang=\"en-CA\" align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">A \u00faltima vers\u00e3o disponibilizada pelo IBGE \u00e9 o modelo geoidal <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ibge.gov.br\/geociencias\/informacoes-sobre-posicionamento-geodesico\/servicos-para-posicionamento-geodesico\/10855-modelo-de-ondulacao-geoidal.html?=&amp;t=o-que-e\">MAPGEO2015<\/a><\/span>. Veja o mesmo na imagem abaixo.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3890\" src=\"http:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2019\/12\/modelo-geoidal-MAPGEO2015.gif\" alt=\"modelo geoidal MAPGEO2015\" width=\"600\" height=\"622\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Juntamente com este \u00faltimo modelo, o IBGE trouxe uma grande novidade. Isso porque tamb\u00e9m \u00e9 poss\u00edvel calcular-se a <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/blog\/ondulacao-geoidal-o-que-e-e-como-calcular\/\">ondula\u00e7\u00e3o geoidal<\/a><\/span> a partir do site do IBGE no link: <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.ibge.gov.br\/geociencias\/modelos-digitais-de-superficie\/modelos-digitais-de-superficie\/10855-modelo-de-ondulacao-geoidal.html\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/ww2.ibge.gov.br\/mapgeo\/mapgeo.htm<\/a><\/span>.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">Ap\u00f3s o usu\u00e1rio enviar os dados para o aplicativo online, o site do IBGE faz a transforma\u00e7\u00e3o dos mesmos, sendo que os resultados s\u00e3o disponibilizados via download atrav\u00e9s de um link. <\/span><\/p>\n<p align=\"justify\"><span style=\"font-size: 20px; font-family: arial, helvetica, sans-serif; color: #000000; line-height: 1.3;\">P.S.: Dependendo da quantidade de pontos submetidos ao servi\u00e7o, o processamento dos mesmos pode levar alguns minutos.<\/span><\/p>\n<p align=\"justify\">\n<h2 style=\"text-align: center;\"><span style=\"font-size: 24px; color: #000000;\"><strong><span style=\"font-family: arial, helvetica, sans-serif;\">Modelos geoidais utilizados no Brasil<\/span><\/strong><\/span><\/h2>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">O Brasil j\u00e1 teve v\u00e1rios modelos geoidais. Isso porque conforme a tecnologia evoluiu, a mesma possibilitou uma melhor determina\u00e7\u00e3o da gravidade terrestre. Como consequ\u00eancia, modelos mais acurados surgiram.<\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Os diferentes modelos geoidais adotados pelo Brasil s\u00e3o:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">MAPGEO92;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">MAPGEO2004;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">MAPGEO2010 e;<\/span><\/li>\n<li><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">MAPGEO2015. <\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Este \u00faltimo serviu de base para o desenvolvimento do modelo mais recente,<span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/biblioteca.ibge.gov.br\/index.php\/biblioteca-catalogo?view=detalhes&amp;id=2101841\"> hgeoHNOR2020<\/a><\/span>, que inaugura uma nova s\u00e9rie de modelos caracterizados pela melhor adapta\u00e7\u00e3o \u00e0s altitudes vigentes na Rede Altim\u00e9trica de Alta Precis\u00e3o (RAAP). <\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">V\u00eddeo sobre o tema:<\/span><\/p>\n<p><center><iframe width=\"728\" height=\"410\" src=\"https:\/\/www.youtube.com\/embed\/ZGY60HC906g\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"text-align: center;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000; font-size: 24px;\"><strong>Domine a Topografia Cadastral atrav\u00e9s de um livro formado por centenas de exemplos pr\u00e1ticos <\/strong><\/span><\/h2>\n<h2 style=\"text-align: center;\"><span style=\"font-size: 20px;\"><a href=\"https:\/\/adenilsongiovanini.com.br\/georreferenciamento-de-imoveis-rurais-na-pratica\/\" rel=\"nofollow noreferrer\"><img decoding=\"async\" class=\"aligncenter size-large wp-image-19317\" src=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-1024x474.png\" sizes=\"(max-width: 1024px) 100vw, 1024px\" srcset=\"https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-1024x474.png 1024w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-300x139.png 300w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-768x355.png 768w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-1536x711.png 1536w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-320x148.png 320w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-640x296.png 640w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-360x167.png 360w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-720x333.png 720w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-1080x500.png 1080w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-800x370.png 800w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento-1280x592.png 1280w, https:\/\/adenilsongiovanini.com.br\/blog\/wp-content\/uploads\/2021\/04\/livro-de-topografia-e-georreferenciamento.png 1565w\" alt=\"livro de topografia e georreferenciamento\" width=\"1024\" height=\"474\" \/><\/a><\/span><\/h2>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Voc\u00ea quer dominar a Topografia Cadastral?<\/span><\/p>\n<p><span style=\"font-family: arial, helvetica, sans-serif; font-size: 20px; color: #000000;\">Ent\u00e3o eu tenho uma \u00f3tima noticia para voc\u00ea. Me refiro ao <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/adenilsongiovanini.com.br\/georreferenciamento-de-imoveis-rurais-na-pratica\/\" rel=\"nofollow noreferrer\">livro Topografia Cadastral e Georreferenciamento de Im\u00f3veis Rurais na Pr\u00e1tica<\/a><\/span>.<\/span><\/p>\n<p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">O mesmo \u00e9 dividido em 10 cap\u00edtulos recheados com muitos estudos de caso e exemplos pr\u00e1ticos. D\u00ea uma espiadinha no sum\u00e1rio do mesmo:<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><center><iframe width=\"99%\" height=\"980\" src=\"https:\/\/drive.google.com\/file\/d\/1HJ8fZz1PvPmftfXHJNFTvIBBzY_FZhPJ\/preview\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/center><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 20px;\"><span style=\"font-family: arial, helvetica, sans-serif; color: #000000;\">Para conhecer melhor a estrutura do livro, juntar-se a mais de 800 profissionais e adquirir sua c\u00f3pia \u00e9 s\u00f3 clicar no bot\u00e3o abaixo:<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000; font-size: 20px;\"><div class=\"su-button-center\"><a href=\"https:\/\/adenilsongiovanini.com.br\/georreferenciamento-de-imoveis-rurais-na-pratica\/\" class=\"su-button su-button-style-3d\" style=\"color:#000000;background-color:#2BCC2F;border-color:#23a426;border-radius:9px\" target=\"_blank\" rel=\"nofollow\" id=\"1\"><span style=\"color:#000000;padding:0px 24px;font-size:18px;line-height:36px;border-color:#6bdc6e;border-radius:9px;text-shadow:0px 0px 0px #000000\"> \u279c Quero Conhecer Melhor o Livro, Pois Quero e Preciso Aprender Mais Sobre Legisla\u00e7\u00e3o Cadastral e Geo. de Im\u00f3veis Rurais<\/span><\/a><\/div><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Modelo geoidal, voc\u00ea acabou de encontrar um artigo definitivo sobre o tema: Com a leitura do mesmo voc\u00ea aprender\u00e1: O que \u00e9 um modelo geoidal; O que \u00e9 o Geoide; Qual o conceito de Elipsoide; Qual a diferen\u00e7a entre altitude ortom\u00e9trica e altitude geom\u00e9trica e; Quais os modelos geoidais utilizados [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3883,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[13,53],"tags":[],"class_list":["post-26187","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arcgis","category-cartografia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Modelo Geoidal? - Adenilson Giovanini<\/title>\n<meta name=\"description\" content=\"Descubra o que \u00e9 um modelo geoidal, qual sua utiliza\u00e7\u00e3o pr\u00e1tica, que dados s\u00e3o utilizados e qual o oficial do Brasil. 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