Tarny is a plant grown in fields on Dorne. There were tarny fields near New Nerra. Tarny roots are edible, and are often fed to horses. In the alternative future Dorne Nanny's Pride farm grew and sold tarny roots.
The Golden Door
A woman from Fleet asked FitzFee's daughter Popsy ikf is she wanted to help feed the town's horses tarny roots, since they had been frightened by the recent Gifter attack, and the horses had always liked Popsy.
The Silver Door
Four-Eyes sold and traded Nanny's Pride Tarny Roots. Four-Eyes wanted to trade five shivs of tarny roots, half a shiv of sea biscuit and some traveller's weed for Bones' bloodhog skull, but the people of the Den did not think it was enough.