Let's see five words: 早上，晚上，中午，上午，下午。 The first two words 早上&晚上，上 is no meaning in these words, so we use neutral tone. But 上 in 上午 do have meaning, like above noon or befere noon, so is forth tone. Anyway, the neutral tone is come from forth tone. If you prounce zǎoshàng instead of zǎoshang, is not a big deal. That's why you can see two versions of the pronunciation.

早上 好! = zǎo-shang hǎo!

早上好 It's natural to pronounciate "上" less stressed than "早" and "好". So "zǎo shang hǎo" is better. But actual sound differnece between them is minor.

According to 现代汉语词典, the most authoritative dictionary on modern Chinese, the correct pinyin for it is zǎo shang hǎo. This means that people usually pronounce the 上 in 早上 very quickly compared to the 早. However, zǎo shàng hǎ would also make sense.

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