Calculation of Monthly, Annual, and Period-of-Record Statistics
by Brad Garner, Hydrologist, USGS
The automated process for computing estimated streamflow to Chesapeake Bay involves calculation of statistics of the data. These summary values are used in plots and tables through this website.
Monthly Mean Streamflow
The relation curves of Bue (1968) for estimating streamflow entering Chesapeake Bay were developed using monthly mean streamflow data. However, streamflow is an instantaneous measurement, typically made every 15 minutes. To obtain monthly mean values:
- One day of instantaneous streamflow values are compiled (typically, 96 measurements at 15-minute intervals).
- The arithmetic mean of these 96 measurements is calculated to obtain a daily mean streamflow value.
- Steps 1 and 2 are repeated for all days.
- A hydrographer reviews daily mean values, adjusts or qualifies them as needed, and publishes and archives them.
- Daily mean values are grouped by month (28 to 31 values per group).
- The arithmetic mean is calculated for each monthly group to obtain monthly mean streamflow values.
Steps 1 through 4 are performed within one year of measurement of instantaneous values, with resulting daily mean values published in the USGS Annual Data Report. Steps 5 and 6 are fully automated and are performed periodically by software.
Annual-Mean Summary Statistics
Summary statistics of streamflow — minimum, maximum, arithmetic mean, 25th percentile, and 75th percentile — are calculated on an annual basis for daily mean or monthly mean streamflow data. When possible, daily mean streamflow data are used, and the calculations do not use any weighting.
When only monthly mean data are available — for example, estimated streamflow entering Chesapeake Bay — they are used to calculate annual summary statistics. For the arithmetic mean, each monthly value is weighted by the number of days in that month.
Period-of-Record Summary Statistics
Summary statistics of streamflow also are calculated for the full period of record using annual-mean streamflow data. The period of record ranges from October 1936 up to but not including the current month. These calculations are straightforward and do not use any weighting.