Quantitative Wildfire Risk Assessment (QWRA) Technical Documentation

Calculating Relative Importance Per Pixel (RIPP)

In order to calculate Conditional Weighted NVC, first the Relative Importance Per Pixel (RIPP) needs to be calculated. RIPP takes into account the Relative Importance (RI) values for both Primary HVRA Categories and the Sub-HVRAs entered in the application, as well as the Relative Extent (RE) which is the number of burnable pixels in each Sub-HVRA footprint. We include the calculated RIPP values within the download package.

There are a three steps involved in calculating RIPP:

RIPP Calculation Step 1

The first relies on the Primary HVRA Category RI values to calculate ‘Of1M.’ In the example spreadsheet, the ‘Primary HVRA RI’ is what was entered into the IFTDSS interface. The ‘Percent of total Primary RI’ is the percentage of the given Primary HVRA RI relative to the sum of all the Primary HVRA RI values. And ‘Of1M’ is the ‘Percent of total Primary RI’ multiplied by 1,000,000.

Primary HVRA "Communities" row outlined in Red, the Of1M value for that row is 281,690.

For example, we will illustrate the calculations for Communities:

‘Of1MCommunities’ = (Primary HVRA RICommunities / (Primary HVRA RIWilderness + Primary HVRA RIAir Quality + Primary HVRA RI Infrastructure + Primary HVRA RI Recreation + Primary HVRA RI Communities + Primary HVRA RI Ecosystem Function + Primary HVRA RI RCW + Primary HVRA RI Salamanders)) * 1,000,000

= (100 / (20 + 20 + 100 +15 + 100 + 40 +40 + 20)) * 1,000,000

= 0.281690 * 1,000,000

= 281,690

RIPP Calculation Step 2

Second, the sum product of the Sub-HVRA RE and RI are calculated for each Primary HVRA Category independently. For this calculation, the ‘Sub-HVRA RI’ is what was entered into the IFTDSS interface. This value is divided by 100, ‘Sub-HVRA RI / 100’. Then that is multiplied by the ‘Relative Extent (pixels)’ to get the ‘Sum’. Finally the ‘Sum Product” is calculated, which is the product of the summed values within a given Primary HVRA Category.

the three "Communities" Sub-HVRA rows are outlined in red, their Sum Product is 44,093.

We will continue with the Communities example:

‘Sum Product Communities’ = ((Sub HVRA RI Low /100) * RE Low) + (Sub HVRA RI Moderate /100) * RE Moderate) + (Sub HVRA RI High /100) * RE High)

= ((0.2 * 135,842) + (0.5 * 25,039) + (1 * 4,405))

= 27,168 + 12,520 + 4,405

= 44,093

RIPP Calculation Step 3

Third, to calculate the RIPP for a given Sub-HVRA, the ‘Of1M’, ‘Sum Product’ and ‘Sub-HVRA RI / 100’ are used.

The "Communities" row is outlined in red, its RIPP value is 1.2777.

We will continue with the Communities example calculating RIPP for the Low Sub-HVRA.

RIPP Low = (‘Of1M Communities’ / ‘Sum Product Communities’) * (Sub HVRA RI Low /100))

= (281,690 / 44,093) * 0.2

=1.2777

Calculating Conditional Weighted NVC

Conditional Weighted NVC (C(wNVC)) is conditional on a fire occurring, therefore it does not include Burn Probability in the calculation. C(wNVC) is calculated for each pixel using the Proportion of Flame Length outputs from Landscape Burn Probability model outputs, Response Functions (RF) and Relative Importance Per Pixel (RIPP) for all Sub-HVRAs present.

Conditional Weighted NVC = ΣΣ RIPP * (RF * Proportion of Flame Length)

Conditional Weighted NVC is the sum of the product of RIPP, Response Functions and Proportion of Flame Lengths (by class) for all Sub-HVRAs present.

We will use the values in the from identify Identify in addition to the *.csv file that is included in the Risk Assessment download which includes the RF and RIPP to illustrate how C(wNVC) is calculated for a single pixel. In the example, the pixel overlaps three Sub-HVRAS: Threatened Vertebrates (Threat Vert P, black), Endangered Vertebrates (Endg Vert P, purple), and All Positive, decreasing slightly (EF2, orange).

QWRA data used in our Conditional Weighted NVC example calculation. Arrows pointing to certain information are color coded to match the example here, Conitional Weighted NVC with green, Sub-HVRA Ecosystem Function in orange, Sub-HVRA Wildlife Endangered Vertibrate in black, and Sub-HVRA Wildlife Threatened Vertibrate in purple. Black orange and purple arrows also point to the Proportion of Flame Length classes

Spreadsheet with values used in the Conditional Weighted NVC example calculation. Sub-HVRA rows are outlined in colors that correspond to those used in the example calculation on this page, "Threatened Vertebrate" row is highlighted in black, "Endangered Vertebrate" in purple, and "All positive, decreasing slightly" in orange.

Conditional Weighted NVC = ((1.046 * ((20 * 0.091) + (10 * 0.545) + (0 * 0.273) + (-40 * 0.091) + (-60 * 0) + (-80 * 0.0))) + ((0.7845 * ((20 * 0.091) + (10 * 0.545) + (0 * 0.273) + (-40 * 0.091) + (-60 * 0) + (-80 * 0.0))) + ((0.1384 * ((100 * 0.091) + (100 * 0.545) + (100 * 0.273) + (90 * 0.091) + (80 * 0) + (70 * 0.0)))

= (1.046 * (1.82 + 5.45 + 0 + -3.64 + 0 + 0)) + (0.7845 * (1.82 + 5.45 + 0 + -3.64 + 0 + 0))) + (0.1384 * (9.1 + 54.5 + 27.3 + 8.19 + 0 + 0))

= 3.797 + 2.848 + 13.714

= 20.359

The graphic below demonstrates the same calculation process in a visual format that might be easier for some to follow.

Table with calculations outlined in colors corresponding to the QWRA data in the Identify image for our C(wNVC) example. Threatened Vertibrate in black, Endangered Vertibrate in purple, All Positive Decreasing Slighly in Orange. The three Sub-HVRA NVC calculations add up to the C(wNVC) value outlined in green.

Calculating Expected Weighted NVC

Expected Weighted NVC is where the likelihood leg of the Risk Assessment triangle comes in. Quite simply, it is the product of Burn Probability and Conditional Weighted NVC. The value is calculated for each pixel in the analysis area.

Expected Weighted NVC = Burn Probability × Conditional Expected NVC

We will use the values from identify Identify, shown below, to illustrate how E(wNVC) is calculated for a single pixel.

QWRA data in the Identify box for our Expected Weighted NVC calculation exampe. Colored arrows point to values described in our example for E(wNVC) and correspond to the values in the example. Green points to Conditional Weighted NVC, Blue points to Expected Weighted NVC, and Red points to Burn Probability.

Expected Weighted NVC = 0.00167 x –49.342

= -0.083