Sampling algorithm

The relative changes in average annual burn fraction act as targets that the sampling algorithm aims to achieve. The algorithm swaps, adds and removes events within the current 10,000-year catalog until all the ecoregion targets are achieved. Some events can occur in multiple ecoregions, as many as three ecoregions in the U.S. model, which suggests the need to sample on multiple ecoregions simultaneously. However, most events only affect one ecoregion, so to simplify the algorithm, events that occur in more than one ecoregion are tagged with the ecoregion that most of their burned area occurs in. This allows the algorithm to work sequentially through each ecoregion to achieve the targets.

Whole years-worth of events are swapped to achieve each annual-based target. To reach larger targets, the same years-worth of events can be sampled multiple times.

Each year in the U.S. wildfire catalog can be traced to a seed year between 1981 and 2015. To preserve the relationships between adjacent seed years during sampling, the selected years-worth of events can only be swapped with another years-worth that shares the same historical seed year or a seed year either side of the same year. For example, if stochastic year 2 is selected, its seed year is 1982, so these events can only be swapped with events that occurred in a stochastic year from 1981, 1982 or 1983. Events with a 1981 seed year can only swap with 1981 or 1982, and events with a 2015 seed year can only swap with 2014 or 2015. This means that in any given year of the sampled catalog the ecoregions share the weather conditions that came from the same historical seed year or one year either side of the seed year.

The final sampled catalogs are tables of stochastic year and event IDs where the years range from to 1 to 10,000 and the event IDs belong to any of the events in the 10,000-year catalog.

The algorithm itself is a variant of the hill climbing algorithm (Burke and Kendall, 2005). The procedure is analogous to shuffling a hand of cards taken from a deck of cards. The initial hand that is dealt is the current 10,000-year catalog. The deck in this case is the 10,000-year catalog but unlike in normal card games, the same card in the deck can be sampled many times, technically known as sampling with replacement. Below are the steps taken to reach the ecoregion targets:

  1. Starting with the initial hand, move to the first ecoregion on the list. If the target average annual burned fraction is different from what is in the initial hand, then sampling must occur.
  2. Select a year at random from the hand and attempt to swap it with a random year from the deck that has the same historical seed year or one year either side as the year selected from the hand. If the swap gets the ecoregion closer to the target burned area, the swap is made, otherwise another year is picked from the hand.
  3. Step 2 is repeated until the ecoregion target is achieved within a tolerance of 0.1%. The algorithm then moves to the next ecoregion.
  4. Steps 2 and 3 are repeated until all ecoregion targets are achieved.

The final set, the 10,000-year climate change conditioned catalog, gives the years of events that occur in each ecoregion. These events are brought into the catalog and are assigned the original stochastic year of the events that they replaced.

A maximum limit is set on the number of times that an event can be sampled from the 10,000-year catalog. If this limit is too low, the larger targets will not be reached, but if it is too high, there will not be enough variability in the catalog for that ecoregion. A limit of 35 is used here.

For each scenario and time-horizon, 50 sampled catalogs were created and the catalog closest to matching the median industry Average Annual Loss (AAL) of the U.S. counties, for that scenario and time-horizon, was selected to represent that scenario and time-horizon. The selected catalogs are used to create the mapping files in the Climate Change Projections. The industry losses were obtained by running the Verisk U.S. Industry Exposure Database through the 10,000-year Verisk Wildfire Model for the United States in Touchstone and are made available in TouchstoneRe.