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At present, commonly used ZTD forecasting models comprise empirical, meteorological parameter, and neural network models. The empirical model can only fit approximate periodic variations, and its accuracy is relatively low. The accuracy of the meteorological parameter model depends heavily on the accuracy of the meteorological parameters. The recurrent neural network (RNN) is suitable for short-term series data prediction, but for long-term series, the ZTD prediction accuracy is clearly reduced. Long short-term memory (LSTM) has superior forecasting accuracy for long-term ZTD series; however, the LSTM model is complex, cannot be parallelized, and is time-consuming. In this study, we propose a novel ZTD time-series forecasting utilizing transformer-based machine-learning methods that are popular in natural language processing (NLP) and forecasting global ZTD, the training parameters provided by the global geodetic observing system (GGOS). The proposed transformer model leverages self-attention mechanisms by encoder and decoder modules to learn complex patterns and dynamics from long ZTD time series. The numeric results showed that the root mean square error (RMSE) of the forecasting ZTD results were 1.8 cm and mean bias, STD, MAE, and R 0.0, 1.7, 1.3, and 0.95, respectively, which is superior to that of the LSTM, RNN, convolutional neural network (CNN), and GPT3 series models. We investigated the global distribution of these accuracy indicators, and the results demonstrated that the accuracy in continents was superior to maritime space transformer ZTD forecasting model accuracy at high latitudes superior to that at low latitude. In addition to the overall accuracy improvement, the proposed transformer ZTD forecast model also mitigates the accuracy variations in space and time, thereby guaranteeing high accuracy globally. This study provides a novel method to estimate the ZTD, which could potentially contribute to precise GNSS positioning and meteorology.<\/jats:p>","DOI":"10.3390\/rs14143335","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T03:50:36Z","timestamp":1657597836000},"page":"3335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Transformer-Based Global Zenith Tropospheric Delay Forecasting Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5043-1536","authenticated-orcid":false,"given":"Huan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7723-4601","authenticated-orcid":false,"given":"Yibin","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"},{"name":"Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China"}]},{"given":"Chaoqian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3566-6668","authenticated-orcid":false,"given":"Wei","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Business and Administration, North China Electric Power University, Baoding 071003, China"}]},{"given":"Junbo","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,11]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"An advanced residual error model for tropospheric delay estimation","volume":"24","author":"Ambrus","year":"2020","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s10291-014-0403-7","article-title":"Development of an improved empirical model for slant delays in the troposphere (GPT2w)","volume":"19","author":"Schindelegger","year":"2015","journal-title":"GPS Solut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00190-017-1066-2","article-title":"VMF3\/GPT3: Refined discrete and empirical troposphere mapping functions","volume":"92","author":"Landskron","year":"2018","journal-title":"J. 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