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Good question. I think....positive Convenience yield will result in backwardation meaning that the future price is less than the spot since there is value in excess of the RFR to hold the asset. That will effect roll yield

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Convenience yield is a function of the carry cost. Carry Cost = Cost of Storage - Convenience Yield. As the convenience yield of a commodity increases the Futures contract will decline in value because the seller is receiving more benefit as they hold on to the underlying asset. As Thecondont pointed out I would think that when the convenience yield increases it will further devalue the futures contract and create a backwardation scenario provided that the contract is below the present spot price.

I wouldn't say that an increasing convenience yield would always result in backwardation, but it should always increase the positive roll yield or reduce the negative roll yield if that particular commodity is currently in contango.

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