GZipStream works when writing to FileStream, but not MemoryStream

If compress some json text, and write that it to a file using a FileStream I get the expected results. However, I do not want to write to disk. I simply want to memorystream of the compressed data.

Compression to FileStream:

string json = Resource1.json;

using (MemoryStream input = new MemoryStream(Encoding.UTF8.GetBytes(json)))
using (FileStream output = File.Create(@"C:\Users\roarker\Desktop\output.json.gz"))
{
    using (GZipStream compression = new GZipStream(output, CompressionMode.Compress))
    {
        input.CopyTo(compression);
    }
}

Above works. Below, the output memory stream is length 10 and results in an empty .gz file.

string json = Resource1.json;

using (MemoryStream input = new MemoryStream(Encoding.UTF8.GetBytes(json)))
using (MemoryStream output = new MemoryStream())
{
    using (GZipStream compression = new GZipStream(output, CompressionMode.Compress))
    {
        input.CopyTo(compression);

        byte[] bytes = output.ToArray();
    }
}

EDIT: Moving output.ToArray() outside the inner using clause seems to work. However, this closes the output stream for most usage. IE:

        using (MemoryStream input = new MemoryStream(Encoding.UTF8.GetBytes(json)))
        using (MemoryStream output = new MemoryStream())
        {
            using (GZipStream compression = new GZipStream(output, CompressionMode.Compress))
            {
                input.CopyTo(compression);
            }
            WriteToFile(output);
        }

where :

    public static void WriteToFile(Stream stream)
    {
        using (FileStream output = File.Create(@"C:\Users\roarker\Desktop\output.json.gz"))
        {
            stream.CopyTo(output);
        }
    }

This will fail on stream.CopyTo because the stream has been closed. I know I could make a new Stream from bytes of output.ToArray(), but why is this necessary? why does ToArray() work when the stream is closed?

Final Edit:

Just needed to use the contructor of the GZipStream with the leaveOpen parameter.