The phrase "monthly timescales" refers to the measurement or observation of events or processes on a monthly basis. It means looking at things that occur or change over a period of one month. Full definition
However, not all aspects of the time series of the annular modes are consistent with a red - noise process with a 10 day timescale: e.g., the annular modes exhibit enhanced variability on monthly timescales during seasons of rigorous stratosphere / troposphere coupling (see section on Stratosphere / troposphere coupling, below); and both annular modes have exhibited trends over the past few decades towards their high index polarities (see section on Climate Change, below). (atmos.colostate.edu)
And there have been a couple instances now where nuclear plants have had to be run below capacity over monthly timescales due to a drought - induced lack of cooling capacity. (realclimate.org)
The approach of the researchers has been to identify climate drivers of vegetation productivity on monthly timescales. (sciencedaily.com)