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A simple sharpening filter seeks out edges and increases the contrast around them. A JPEG is a “lossy” format, meaning it cuts the file size by tossing out superfluous data, leaving you with varying-sized single-color squares in areas of the image where there is no edge. This means that where there’s an edge in a heavily “jpegged” image, you’ll end up finding lots of these squares, which adds to the amount of edges for the sharpening filter to find. If you look at the original photo OP posted, there’s a bunch of “grainy” spots where it found a JPEG edge and bumped up the contrast.
To compensate for this, I used Photoshop’s “Smart Blur” — which maintains hard edges but eliminates grain — on the sky. I then used the “Motion Blur” filter on the grass, matching the direction of the blur with the average direction of the grass. I then used “Unsharp Mask” on the grass to give it some definition.