In IaaS Cloud Computing platforms, elasticity offers to users the possibility to adjust the number of resources to the current workload, taking into account peak and trough periods (high and low activity) by powering down/up some resources. In previous work, we solved the challenges raised by the extension of elasticity to storage resources in the context of static data popularities. In this paper, we address the same challenges in the context of dynamic data popularities. We propose 3 solutions that estimate the data popularities, and an algorithm that reduces or increases the number of used server according to the period activity. Based on the platform cost (the resources are paid for the time they are used), our simulations on top of SimGrid show that we could either improve HDFS' performance by up to 99% while providing similar cost, or we could reduce cost up to 50% while providing similar performance.