the problem is this, whereas I am a newbie of this argument. I don't know
what do you mean with "the image needs to be in the same projections" as
your base layers. You mentioned to "create a layer in Geoserver from the
image" or "doing it in the proper image transformation tools". Also I don't
know what do you mean with " 400x400km on the ground or 400x400 projected
kms". I am sorry, probably there are some assumptions that I should know
that I am completely ignoring. What I know is only that I have a png image
400x400 pixels, each pixel is a km so it represents a linear square area of
400x400 kilometers and I have to draw it centered in a specific lat/lon
point.
This comes down to really understanding what your image is. A figure that precisely represents 400x400 kilometers on the ground could not be a square. That's the reality of going from an ellipsoidal object to a flat image. So your 400x400 image is a projection of the ellipsoid onto a flat plane. The question is which projection - because you need to know that to get the image reprojected accurately. It will also depend on your own precision needs. If the image is derived from satellite or aerial photography then you need to find out what the rectification process (if any - though if you know it is 1px=1km then I will bet it has some). If the image is a construct (say from modelling), then it comes down to what assumption were made building the grid - the implicit projection used.

The question about projected meters versus ground meters is at the heart of projection. Consider 900913 - this is a variant of the mercator projection. If you measure the a distance on the map at the equator, it will correspond well with the distance on the ground. However, if you measure a map distance at a latitude of 70degrees, then the map distance will be very much larger than real distance. (So Greenland looks much larger than it really is on a mercator map). A printed mercator map in an atlas will have a scale correction for latitude. You might want to look at a projection primer like http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html My bible is Snyder's "Map projections - a working manual".

Regarding tools. You will find the tools in all commercial GIS that I am aware of. ERDAS is what we use for photos and remote sensing stuff. Also commonly use ArcGIS. You will probably find adequate tools in GDAL and GMT in the freeware. I would strongly emphasis however, that you need to understand your image first. Normally you would enter the coordinates of the 4 corners of the image. At 1px per km, you could probably get away with pretty naive calculation of those coordinates for model output. Will be tougher if this is remote sensing imagery where you might get visible mismatch with google imagery.

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