Location and Duration for Event Ranking

The next step is to select the location used to rank the events/years in the historical record by maximum volume, and set the duration of that volume. The historical record is ranked to identify the largest events, and those events contribute a portion of their allotted incremental probability to the set of synthetic events. (If use of serial correlation is selected, that specified correlation will be maintained with that ranking of events by this Location for a defined Season. Refer to the Serial Correlation of Events section for more information.) Generally, the selected location should be significant, since it is used by the Hydrologic Sampler to represent the watershed as a whole. Note, while the time series provided for the Bootstrapping Historical/Synthetic Basin-wide Events sampling method generally consists of system inflows needed in the watershed models, the user can include an additional location with a time series for the ranking that is not needed as model input (e.g., total channel flow).

  1. From the Hydrologic Sampling Editor, from the Settings tab, Hydrographs sub-tab, Ranking of Historical Record Events panel, from the Location for event ranking list select a hydrograph location.  This location will be used to rank the historic events to determine their exceedance probability used for sampling.  Typically this is a location that best represents the watershed as a whole, such as the unregulated flow at the most downstream control point, or the location for which synthetic events were scaled.

    Warning

    Changing the timeseries used for ranking will result in a reordering of the sampled events during the compute.  It is not recommend to change this timeseries while adding additional study alternatives as Hydrologic Sampler will compute a different sequence of years as a result.

  2. From the Flow duration for event ranking (days) list select the appropriate flow duration for the selected hydrograph location. Available options are 1, 2, 3, 5, 7, 15, 30, 45, 60, and 90 days. The Hydrologic Sampler computes the maximum average flow across the selected duration to rank the historical events (Historical Record tab, Adding the Historical Record) from largest to smallest. For all hydrograph locations, repeat Steps 1 and 2.
    Hydrologic Sampling Editor, Bootstrap Sampling, Settings tab, displaying the Hydrographs tab.

Serial Correlation of Events 

If the sequence of events sampled is important, meaning that persistence in hydrology from one water year to the next can impact basin conditions such as reservoir carryover storage, serial correlation of events can be applied to the sampling process. 

This method uses an Autoregressive lag-1, AR(1), model instead of randomly sampling exceedance probabilities to pick the next event.  First, the historical and synthetic events are ranked by a seasonal volume, and their accumulated incremental exceedance probabilities define an empirical volume frequency curve from which events are sampled. Then, an AR(1) process is used to generate a random series of correlated N(0,1) variates as exceedance probabilities, which are used to sample event/years from that empirical frequency curve, creating a series of sampled events with serially correlated event volumes.

  1. To enable this feature, the user must check Use Serial Correlation. This will remove the option to enter the Flow duration for event ranking (days) described above, and does not allow stratified sampling to be used.
  2. The user will then enter a correlation coefficient under the Annual serial correlation field. 
  3. A seasonal volume may be used for sampling by defining the start date and end date of the season over which the water supply volume is measured. 
  4. Checking Apply to uncertainty sub-sample will cause the serial correlation to be applied in sampling of knowledge uncertainty when creating the event pools used for each realization.  Leaving this unchecked only applies annual serial correlation when selecting the final sampled events.
Event sampled with serial correlation cannot span the Start of Water Year date defined at the top of the Hydrologic Sampling Editor.

Hydrologic Sampler Editor Settings Tab with Use Serial Correlation checked.

Uncertainty

Next, define the uncertainty in frequency to use in the Bootstrapping Historical/Synthetic Basin-wide Events sampling method. As described in Bootstrap Sampling with Historical and Pre-scaled Synthetic Events, uncertainty in the frequency description is defined by the sampling error due to limited record length. At the beginning of each realization, a sub-sample of size N that equals Equivalent Years of Record is generated, and then used as the event "bucket" for that realization. All events in the sub-sample are given equal incremental probability, because the sub-sample is a possible realization of an historical record. From the Hydrologic Sampling Editor, from the Uncertainty Method panel, the uncertainty options and the corresponding user inputs required are:

  • No uncertainty – In this case, the sub-sample that captures uncertainty in each realization is not created. All historical record and synthetic events are included in the event "bucket" for all realizations, using their computed or overridden incremental probabilities.
  • Equivalent Years of Record – With this choice, the uncertainty bootstrap described above is activated and the sub-sample that captures uncertainty in each realization is created. The Equivalent Years of Record represents the information available in generating the synthetic events (specifically, assigning their likelihoods), and thus may be longer than the historical record provided to the event "bucket."

Exceedance Probabilities of Synthetic Events

The Exceedance Probabilities of Synthetic Events panel contains a table where the user defines the exceedance probabilities (and corresponding return periods) available for synthetic events (review Defining Synthetic Events). The user does not need to make use of all of the available probabilities when creating synthetic events. Conversely, if a required exceedance probability is not present in the default table, the user may add the desired exceedance probability to the table.

Modifying the Exceedance Probabilities of Synthetic Events table:

  1. From the Hydrologic Sampling Editor, from the Hydrographs tab, from the Exceedance Probabilities of Synthetic Events panel, click New, and the New Exceedance Probability dialog box opens. A new exceedance probability (0-1) can be entered.
  2. Enter the desired exceedance probability, between 0.00 – 1.00, in the Exceedance Probability box, click OK. The New Exceedance Probability dialog box will close and the Exceedance Probabilities of Synthetic Events table updates automatically with the new exceedance probability value and associated return period.
  3. Repeat Steps 1 and 2 until the Exceedance Probabilities of Synthetic Events table contains the desired exceedance probabilities.

To delete exceedance probabilities from the Exceedance Probabilities of Synthetic Events table:

  1. From the Hydrologic Sampling Editor, from the Hydrographs tab, from the Exceedance Probabilities of Synthetic Events panel, select the exceedance probability to delete, click Delete. The Exceedance Probabilities Message window will open. Click Yes to confirm the deletion, the Exceedance Probabilities Message window will close. The table updates with the selected exceedance probability deleted from the table. Repeat this step as necessary to remove individual exceedance probabilities from the table.