A write ordering style asynchronous replication service utilizes a loosely-accurate global clock in a data backup and recovery storage environment. The storage environment includes a set of source storage systems illustratively embodied as source replication nodes that cooperate to maintain a consistency group that may span multiple geographical sites. The storage environment also includes one or more target storage systems illustratively embodied as target replication nodes configured to service the consistency group. The write ordering style service utilizes the loosely-accurate global clock to provide consistent replication of a storage space of the consistency group.