We quantify operational departures as the difference between the OT and actual reservoir levels for each day in the period of record. Reservoir elevations are not comparable between reservoirs because each reservoir has a different topography and volume. However, reservoir volume is linked to elevation through area capacity tables. Thus, operational departures were calculated as a percentage of the OT storage for each day:

            Percent Storage = (Reservoir Volume)/(Operational Target Volume) × 100

A percent storage of 100% indicates that the reservoir is at the OT; less than 100% indicates the reservoir is in shortage while a value greater than 100% indicates a surplus. Since reservoirs redistribute water, fluctuations around the OT are not of primary concern. Rather, we focus on systematic departures from the OT, where systematic departures are defined as when a reservoir is consistently off the OT. The percent storage provided the base for assessing systematic departures. We calculated the minimum, 10th, 25th, 50th, 75th, 90th and maximum reservoir percent storage for each day of the year; essentially creating a continuous boxplot of percent storage statistics.

Annual operational departures over time can be analyzed by applying the concept of flow duration curves, which is a curve quantifying the cumulative percent of time a specified streamflow is equaled or exceeded during a given period. This concept can be modified to display the percent of time the operational target volume is equaled or exceeded within a typical year by calculating the cumulative frequency of departures. Here we calculate the 10th, 25th, 50th, 75th and 90th FDC, with the median reflecting reservoir variability within a “typical” year. The conceptual framework for an ‘expected’ storage duration curve (SDC) would be for the reservoir to remain near 100% for much of the period of record, indicating a small percentage of time with reservoir levels off target. Flood control reservoirs would be expected to have a more extreme tail above the OT as the flood control pool fills to accommodate flood events, while withdrawals for water supply or chronic droughts would increase the amount of time below the OT. Reservoirs spending substantial time off the OT would have a FDC displaced above the OT if consistently storing more water than targeted, and below if depleted more often than targeted.

*Results may differ from the paper depending on time period selected. Target bands for operational targets were not included in the web version.

The period of record (POR) for each reservoir varies based on construction year and data availability. The percent of storage volume relative to the operational target volume was calculated so that at 100% the reservoir volume is at the operational target. The operational departure is calculated by subtracting 100% from the percent storage volume. A positive number indicates the reservoir is in surplus while a negative number indicates deficit. The cumulative sum of the percent storage over time was calculated to determine whether a reservoir has experienced a systematic shift over time.

            Storage Percent = Volume Reservoir / Operational Target Volume * 100%
            Operational Departure Percent = Storage Percent – 100
            Cumulative Departure = ∑ Operational Departure Percent over time

A reservoir that is consistently in surplus mode will have the cumulative departure that increases over time with sharp increases occurring at major flood events. A reservoir that is consistently operating below the operational target will have a cumulative departure that decreases over time with rapid decreases occurring during major drought events. A reservoir that continually operates around the operational target will fluctuate around zero. Lastly, a reservoir may change and shift from one type of operational mode (surplus, shortage, balanced) to another type.

*Results may differ from the paper depending on time period selected. Target bands for operational targets were not included in the web version.

The magnitude of surpluses was calculated relative to the total volume up to the top of the flood control pool and deficits relative to the operational target volume. Surplus volumes go into the flood control pool and so we wanted to include the total volume when assessing the magnitude of surpluses. Whereas deficits should be in relation to the volume of the reservoir meant to be filled; i.e., the storage volume up to the top of the conservation pool as defined by the operational target (OT).

            Departure = Reservoir Volume - OT volume
            Lake Level > OT = Departure/(Flood Control Volume - OT Volume) × 100
            Lake Level < OT = Departure/(OT Volume) × -100

Each reservoir will have three scores since the frequency of departure is calculate relative to the magnitude (<5%, 5-15%, >15%).

1. The y-axis was calculated by taking the median magnitude of departure within each magnitude range (5%, 5-15%, >15%). The values were then scaled and plotted in the chart.
2. The x-axis was calculated by taking the percent of time in the selected period of record that the reservoir was within each magnitude range (5%, 5-15%, >15%).

The highest score (type) is taken as the overall type for the reservoir. The scores were arbitrarily chosen and can be modified to meet your organizations criteria of "significance".

*Results may differ from the paper depending on time period selected. Target bands for operational targets were not included in the web version.