Bootstrap Sampling with Historical and Pre-scaled Synthetic Events

This chapter describes how to set up the Hydrologic Sampler with a flow-sampling alternative using the Bootstrapping Historical/Synthetic Basin-wide Events sampling method. This sampling method randomly samples events from a "bucket" of user-defined historical and optional synthetic basin-wide flood events to provide flood times series for all basin inflow locations within the modeled watershed.

To use the Bootstrapping Historical/Synthetic Basin-wide Events method for hydrologic sampling, concurrent historical time series of flood events are needed at all required watershed inflow locations. Events are randomly sampled from the historical event time series and additional synthetic events (if needed), such that all defined inflow locations use the hydrographs associated with the sampled event/year. This sampling approach is meant to ensure that flood event hydrographs across the watershed can feasibly occur together, and mimic how the flood hydrographs occurred during historic floods, by choosing from events the user has provided. Historical flood events receive a likelihood of 1/N, where N is the number of historical years in the time series. Synthetic events can be developed outside of the Hydrologic Sampler and added to the sampling "bucket". Synthetic events are typically either larger than events in the historical record or defined to represent a different distribution of flow throughout the watershed, and are generated to have a specified exceedance probability. Synthetic events are assigned a likelihood related to their exceedance probability. When synthetic events are included, the sampling probability of the largest historical events is reduced, as described in Section 3.4, to bring the total probability of all events to 1.0, with the logic that the largest events are most similar to the synthetic events, and so can share their likelihood of being randomly selected.

The Bootstrapping Historical/Synthetic Basin-wide Events method maintains flood event frequency by sampling events at the frequency they occurred or would occur, using the incremental likelihoods defined above. Uncertainty in the event frequency relationship is defined by the sampling error due to limited record length (knowledge uncertainty), and is captured once in each realization with a preliminary bootstrap similar to that used in the frequency curve sampling methods (Correlated Flow Frequency Sampling and Precipitation Sampling - Basin Average). A sample of size N is generated by choosing events from the "flood bucket" The N-member sub-sample is a constructed example of the sampling error that might exist in the historical record of flood events available for the watershed. The sub-sample then becomes the new "flood bucket" used to sample event/years for that realization. All events in the sub-sample are given equal incremental probability, though lower probability synthetic events may have been selected, because the sub-sample is a possible realization of an historical record.

By default, the random selection of a flood event in each year of the lifecycle (analysis period) is independent of the previous year. However, the user may choose to define a serial correlation between years. In this case, the temporal relationship of event volume between one year and the next can be maintained as specified using a Autoregressive lag 1 process.

The Bootstrapping Historical/Synthetic Basin-wide Events sampling method also has the option to generate random hydrologic forecasts (e.g., an April-August snowmelt runoff volume) for each event, for cases in which management of projects in the watershed requires those forecasts. Forecast error statistics and starting forecast volumes are required user inputs. The user-defined forecast errors are then randomly sampled and added to the starting forecast volume of the sampled event, producing the randomly deflected hydrologic forecast. The purpose for including the optional ability to generate random forecasts within the Bootstrapping Historical/Synthetic Basin-wide Events method is provided in Sampling Forecast Uncertainty.

With the Bootstrapping Historical/Synthetic Basin-wide Events sampling method selected, the Hydrologic Sampling Editor contains the six method-specific tabs described in the overview table.

Hydrologic Sampling Editor, Flow Sampling, Bootstrapping Historical/Synthetic Basin-wide Events, Location and Parameters tab example.

Hydrologic Sampling Editor, Flow Sampling, Bootstrapping Historical/Synthetic Basin-wide Events, overview table.

Tabs	Tab Description
Locations and Parameters	The purpose of the Locations & Parameters tab is for selecting the Data Locations and specifying the Parameter (variable) type and DSS C-Part for the selected data locations. Parameter types include flow, precipitation (Precip), temperature (Temp), elevation (Elev) and stage. Review the HEC-DSSVue user manual for more information regarding the HEC-DSSVue C-part. Refer to Hydrograph Locations and Parameters for more information.
Settings	The Settings tab is for specifying information about the locations for sampling and some method-specific choices. Refer to Ranking Events, Uncertainty Method, and Synthetic Event Probabilities (Settings tab) for more information. Two tabs are available from the Settings tab: Hydrographs tab – allows the user to choose the location and duration for Ranking of Historical Record Events to determine the largest event, select the Uncertainty Method and specify the Exceedance Probabilities of Synthetic Events as needed. Forecasts (conditional) tab – is only enabled when Include Forecasts has been selected. From the Forecasts tab, the user can Select Forecast Locations at which to generate random forecasts. Forecast Statistics are defined for each selected location: forecast date(s), forecast error statistics and serial and spatial correlation between forecasts.
Historical Record	The Historical Record tab is for providing the time series that represents the record of flows that occurred in the watershed, as well as the record of other selected parameters. Refer to Adding the Historical Record for more information. Two tabs are available from the Historical Record tab: Hydrographs tab – contains the DSS input table for specifying the historical time series DSS records for all of the locations selected in the Settings tab. Forecasts (conditional) tab – is enabled when the Include Forecasts checkbox is selected. The DSS input table allows the user to specify time series of starting forecast values (before random error is added) for each location and forecast date defined on the Settings tab, using the Select DSS Path button.
Synthetic Events	The Synthetic Events tab is used for adding synthetic flood events that are either larger than those in the historical record, or reflect some other feasible and relevant origination of flow throughout the watershed. Any number of synthetic events may be added for a given exceedance probability, and synthetic events may be added for many exceedance probabilities as well. In the Synthetic Events tab, users can add new, rename, copy, or delete existing synthetic events. Refer to Defining Synthetic Events for more information. Two tabs are available from the Synthetic Events tab: Hydrographs tab – contains the DSS input table for specifying input flow time series data (and data for other selected parameters) for synthetic events for all locations selected in the Settings tab using the Select DSS Path button. Forecasts (conditional) tab – is enabled when the Include Forecasts checkbox is selected. The DSS input table allows the user to specify time series of starting forecast values (before random error is added) for each location and forecast date defined on the Settings tab, using the Select DSS Path button.
Synthetic Summary	The Synthetic Summary tab provides two summary tables of the user-defined synthetic events. The summary tables are for viewing purposes only, and the information displayed in the tables cannot be modified from this tab. Refer to Synthetic Summary Tab for more information. The first table has a row for each exceedance probability for which synthetic events have been created. This table contains four columns: exceedance probability, return period, total incremental probability, and adjusted probability assigned to that exceedance probability/return period. The adjusted probability column lists the multiplier used to adjust the probabilities. The second table references the single exceedance probability selected in the first table, and contains the same four columns. This table displays the list of synthetic events created for the exceedance probability, and the weight, subsequent incremental and adjusted probabilities assigned to each event.
Probability Override	The Probability Override (conditional) tab is enabled when the Incremental Probability Override checkbox is selected. The Probability Override tab allows users to modify the incremental probabilities for each of the historical and synthetic events used in the Bootstrapping Historical/Synthetic Basin-wide Events sampling method, and provides a check to ensure the total incremental probability is equal to 1.0. Refer to Selecting Bootstrapping Historical/Synthetic Basin-wide Events method, Incremental Probability Override section for more information.