Are you able to set CMOD the folder /modules/mod_globeweather/mod_globeweather/metar_data by using an FTP client? Try CMOD 777 and just the above folder (i.e. no sub folders). Then access your website again.
Double check the FTP layer settings in your Joomla! global server config. The host is 127.0.0.1 by default but maybe you should enter your 'real' FTP host server here. FTP layer does not need to be enabled. GlobeWeather only reads these settings to try to access the above folder.
