Why do maps of melanoma prevalence correlate negatively with UV index, negatively with ground ozone, and positively with atmospheric ozone levels? What is the causal link behind the correlation of melanoma: negatively with UV index, negatively with ozone in the lower atmosphere, and positively with ozone in the upper atmosphere? Intuitively, melanoma would positively correlate with UV index, and negatively with upper atmospheric ozone. 

Increased melanoma risk with higher latitude seems to be true on a global scale as well as locally in the US, but is reversed locally in the UK and Australia where melanoma rate negatively correlates with latitude. Could high population density and high ozone in the lower atmosphere be affecting a lower risk of melanoma?


It appears melanoma rates do not always negatively correlate with ozone in the upper atmosphere, and positively with high UV index.
It does appear that melanoma sometimes negatively correlates with population density and ozone in the lower atmosphere (caused by pollution in heavily populated areas).


In this study, Chinese individuals living in the US have a higher risk of melanoma than those in China. The map of the United States with the highest rates of skin cancer (below in blue) appears to strongly correlate with a map of ozone in the lower atmosphere (below in orange).


Positively correlating latitude with rate of melanoma (higher towards the poles)


US map from CDC in cases per 100,000

World map from Nature



Negatively correlating latitude and population density with rate of melanoma

UK


UK melanoma rate map from BBC

UK population density map. Population density seems to negatively correlate with melanoma.



Australia


Australia melanoma guidelines from Cancer.org.au stating the north has a higher risk for melanoma. 

Australia population density map. Population density seems to negatively correlate with melanoma.
 


Negatively correlating latitude with UV index (higher towards the equator)




Positively correlating temperate zones with ozone in the upper atmosphere.
I cannot address your specific questions, but with regards to cancer, Cedric Garland has analyzed and presented similar data and attributed a lower incidence of cancer with a higher production of vitamin D at the lower latitudes as a possible reason. Mina Bissel at Berkeley labs and others have discovered that cells in isolation can lead to cancer. The other connecting link is that vitamin D promotes intercellular communications and thus may be aiding whatever process it is that leads to cancer. If you just google these names, vitamin D and cancer, you will find links to most if not all the papers.