Overview

The first three steps of this guide address the natural uncertainty of the forcing conditions (precipitation). For watershed-averaged precipitation frequency, no additional uncertainty needs to be modeled to create the frequency curve. For flow frequency curves, uncertainty within the hydrologic processes must be addressed. There are two key sources of hydrologic uncertainty in these types of hypothetical simulations: parameter uncertainty and initial condition uncertainty. Parameter uncertainty arises due to natural variability in parameters across events or error induced by the way the model process simplifies reality. Initial condition uncertainty occurs because the watershed conditions are not always the same prior to a heavy rainfall event. This guide discusses a method for handling both types of uncertainty in an SST simulation for flow or stage frequency.

Modeling Parameter Uncertainty

A calibration/validation exercise for your watershed model will likely reveal that there is variation in calibrated parameter values across events. Subbasin parameters should be added for each analysis point as a Parameter Value Sample. Parameter values can be taken directly from calibration events or varied based on the modeler's engineering judgement. Each parameter to be sampled, along with each analysis point (subbasin) will require its own table. In the example below, the BigSoos subbasin is the point of interest and six values from six calibration events are being sampled for constant loss, time of concentration and storage coefficient. 

Most important calibration parameters for parameter uncertainty:

• Constant loss rate
• Clark time of concentration and storage coefficient
• Linear reservoir coefficients

Secondarily important parameters that still may be adjusted:

• Linear reservoir layer fraction
• Canopy crop coefficient

Parameters that generally should not be adjusted:

• Max deficit
• Impervious area
• Number of linear reservoirs in a layer
• Maximum canopy storage

When modeling snow, there are a large number of additional parameters, many of which are uncertain and variable. A separate guide discussing snow in the context of SST modeling will be developed. Using the HMS Uncertainty Analysis (UA), we can vary which calibrated parameter set is selected with each SST simulation. It is important to keep the parameters "together" and not mix and match parameters in a basin model from different events. To accomplish this, use either the Specified Values with a Random (Same Index) or Sequential Loop sampling method to keep the parameters with their respective calibration event.

Modeling Initial Condition Uncertainty

Initial conditions present a more complicated case because unlike the calibrated parameters, they should be based purely on the antecedent conditions of the watershed and are not tied to a specific event. To properly sample these initial states, we can make use of a Quasi-Continuous modeling approach. The simplest way to think of this approach as if it is inserting an SST event into the continuous period of record, so that whatever state the watershed is in at that time is a reflection of everything that has happened before it. The primary parameters you should consider when modeling initial condition uncertainty are:

• Initial deficit
• Initial reach flow
• Initial reservoir storage/stage

Secondary parameters may include:

• Initial flow out of baseflow layers
• Initial canopy storage

If you include snow in your model, the number of initial conditions grows significantly. A separate guide discussing snow in the context of SST modeling will be developed. Building a probability distribution to quantify the uncertainty around these parameters, especially when your model contains a large number of subbasins, is challenging. It is especially difficult to define the potential dependency between them.

Quasi-Continuous Modeling Approach Overview

We set up a quasi-continuous model by first creating one that simulates the full available POR of the best available meteorological data, ideally the same source being used to generate the SST catalog. It should be calibrated to the most reasonable extent practicable, acknowledging that continuous calibrations have their own challenges compared to event calibrations. The key to the calibration is that hydrologic states that represent antecedent conditions are well-represented, e.g. soil moisture, reservoir storage, etc. The model can be run at a coarser timestep than the event models (i.e. daily instead of hourly) which saves some computation time and reduces the volume of results.

The results from the POR simulation serve as a "reanalysis" of historical hydrologic conditions. Often, we do not have observed values for all the fluxes and states of the hydrologic cycle. A hydrology model has to simulate all these processes to complete the water balance. We use the hydrology model as a stand-in for observed data and use the modeled values as observed historical states to spin up an event model. The seasonality of the storms in the catalog is linked to the seasonality of watershed conditions, so that conditions more frequently associated with storm events are selected more often.

Implementing Quasi-Continuous Simulation in HEC-HMS

The implementation details below are add-ons to the model setup discussed in the guide titled Fundamentals of Stochastic Storm Transposition. Those steps are still necessary to set up the meteorological portion of the SST simulation. Build and calibrate a continuous model for the watershed and produce a full POR simulation.

1. On the Uncertainty Analysis editor panel, select the Period of Record Simulation Run. State variables from this run will be sampled and translated to a corresponding initial condition
2. From the SST catalog, extract the start date for each of the events and populate a Parameter Value Sample with those dates.
3. Add a parameter for Sample Date using the Storm Dates.
4. Next add a parameter for each of the initial conditions of interest. Use the Time-Series sampling method. This will pull soil moisture states on a given date and use the sampled value as the Initial Deficit for a given simulation within the Uncertainty Analysis. 

This can be done for each initial condition that needs to be sampled. A list of initial states and the initial condition that it represents is shown in the table below.