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I'm adding WorldWind wms services (http://data.worldwind.arc.nasa.gov/wms?) to ArcMap (ArcGIS 10.2.2) but maps are misplaced, looks like they have reversed coordinates (as explained here: http://viswaug.wordpress.com/2009/03/15/reversed-co-ordinate-axis-order-for-epsg4326-vs-crs84-when-requesting-wms-130-images/). Is there any workaround to get maps properly placed?

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You seem to be right and server wants BBOX coordinates in lon-lat order even it claims that it is a WMS 1.3.0 server.

This brings the whole world from east to west http://data.worldwind.arc.nasa.gov/wms?service=WMS&version=1.3.0&request=GetMap&layers=esat&CRS=EPSG:4326&BBOX=-180,-90,180,90&format=image/png&styles=&width=300&height=200

This request with standard compliant axis order does not http://data.worldwind.arc.nasa.gov/wms?service=WMS&version=1.3.0&request=GetMap&layers=esat&CRS=EPSG:4326&BBOX=-90,-180,90,180&format=image/png&styles=&width=300&height=200

However, the GetCapabilities document from the service is not valid. Server seems to support only WMS 1.3.0 but GetCapabilities has a root element which is used in WMS 1.1.1 WMT_MS_Capabilities version="1.3.0" Schema-aware clients cannot contact the service at all. Root element should be WMS_Capabilities version="1.3.0"

I don't know about ArcGIS, but with QGIS you can use the service by selecting "Ignore axis orientation" from server settings.

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