Cloud storage systems are currently very popular, generating a large amount of traffic. Indeed, many companies offer this kind of service, including worldwide providers such as Dropbox, Microsoft and Google. These companies, as well as new providers entering the market, could greatly benefit from knowing typical workload patterns that their services have to face in order to develop more cost-effective solutions. However, despite recent analyses of typical usage patterns and possible performance bottlenecks, no previous work investigated the underlying client processes that generate workload to the system. In this context, this paper proposes a hierarchical two-layer model for representing the Dropbox client behavior. We characterize the statistical parameters of the model using passive measurements gathered in 3 different network vantage points. Our contributions can be applied to support the design of realistic synthetic workloads, thus helping in the development and evaluation of new, well-performing personal cloud storage services.