Purpose and Style

This tutorial is application guide for SST that explains how it can be implemented in the software.

Stochastic Storm Transposition Overview

Stochastic Storm Transposition (SST) is a procedure for expanding available information about the frequency of rainfall extremes by leveraging a large catalog of historical storm events. The catalog samples severe precipitation events from a large, meteorologically homogeneous region around the study watershed called the transposition domain. It is assumed that any storm that occurs within this region can be freely moved via transposition to any other location within the region with equal probability. The region is much larger than the study watershed, which allows storms that did not occur over the study watershed to be transposed there to see their effects. Determining a transposition domain requires expert judgment, although statistically-based procedures that can be used to define a domain in an objective way are under development.

The storm catalog contains all events that exceed "severity criteria" and occurred in the transposition domain, and typically contains many distinct events per year. The criteria are typically chosen so that the catalog contains, on average, 5-15 storm events per year. Ideally, the precipitation data being used will have a long period of record such that the catalog contains hundreds of events. 72 hours is the typical storm duration. A threshold of potential precipitation is selected to achieve a target rate of events per year; for example selecting a threshold that results in 400 storms in a 40 year record, giving an average of 10 storms per year.

HEC-HMS Implementation

HEC-HMS uses a simulation type called the Uncertainty Analysis (UA) to allow for systematic variation of model parameters. In HMS, the Meteorologic Model controls how atmospheric boundary conditions are served up to the basin model. Depending on the processes the user selects for their met model, there are a number of parameters they can control (or can be controlled by the UA). The Gridded Precipitation method for the Precipitation process has a number of controls that allow the user to select which precipitation data to apply, shift it in time, and shift it in space. These features were added by the HMS team to make hypothetical modeling with observed gridded precipitation events easy. The parameters of the Gridded Precipitation method that the UA controls in an SST simulation are the data source (storm event) and its transposition location. The UA has several ways it can vary parameters in all parts of the model, including sampling from probability distribution, reading through a list of values, and so on. Its random sampling scheme allows the user to set an initial seed that ensures that the simulation is repeatable as long as the seed and all other settings remain the same. Meteorlogic model parameters are not the only things the UA can control. More frequently it is used to explore hydrologic uncertainty by varying basin model parameters. The section Hydrologic Uncertainty will discuss an approach to using the UA to capture parameter and initial condition uncertainty in conjunction with an SST simulation. The UA does not have any notion of years or realizations. It has one setting for simulation size which is the total number of samples. This means that the results will need to be post-processed in some manner to make sense of them (see Post Processing the Results).

Key Differences from the Traditional "Design Storm" Approach

Many flow frequency studies have been developed using point precipitation-frequency derived design storms based on products like NOAA Atlas 14. The major assumption being made in those analyses is that the frequency of the storm is equal to the frequency of the flow. In other words, if I develop a design storm with a depth equal to the 100-year rainfall for my location, the flow that results from applying it to my basin model is also the 100-year flow. It is also assumed that an area-averaged precipitation frequency relationship can be created by using the point frequency product and applying an area reduction factor (ARF) appropriate for the watershed area. Neglecting to use ARF when applying point precipitation-frequency products is one of the most common pitfalls in their application. Traditional design storms also require the modeler to chose appropriate spatial and temporal patterns to turn a total storm depth (or several incremental depths for a range of durations of accumulation) into something that can be used as a boundary condition for a hydrologic model.

SST makes no such assumptions. It attempts to replicate the "natural" processes of precipitation generation in a region and avoids making "engineering choices" or assumptions to take a design criteria and turn it into something that looks like a real storm - because it is a real storm. The two fundamental assumptions are 1) that the transposition domain is homogeneous, and 2) the selected severity criteria will generate the desired frequency response (whether precipitation or flow/stage.) Both assumptions can be tested using sensitivity analysis.

SST Simulation Structure

SST is based on Monte Carlo simulation, a statistical procedure that uses large samples to approximate the behavior of a probability distribution. Each storm and its re-positioning is a sample of the population of possible storm occurrences with an unknown (and unknowable) probability distribution. The sampling procedure is based on a technique called the block bootstrap that re-samples storms from the catalog in their entirety, preserving their space-time structures.

From the bottom up, SST simulations are structured like so:

• Each event is an equal-chance selection of storm from the catalog with an equal-chance placement of the storm inside the transposition domain
  • The storm's precipitation interaction with the study watershed can be captured
  • Optionally, hydrologic processes can be simulated to capture flood responses
• Each synthetic year is a number of events that depends on the size of the catalog
  • The number of events is either random (drawn from a distribution) or fixed at the average rate of storms in the catalog
  • Annual maximum statistics are computed as the maximum of all events in the year, whatever the statistic
• Each realization is a number of synthetic years that determines the quality of estimates for rare frequencies
  • The number of synthetic years should be much larger than the rarest average return interval (ARI) of interest
• A full uncertainty simulation will have multiple realizations
  • For SST, this process captures Monte Carlo error