Relative Frequency Score (RFS)
The rarity and magnitude of a hazardous weather event is an often sought after piece of information as this places individual events in a greater historical context. As it turns out, there have been several attempts to quantify both rarity and magnitude so that major events can be compared to each other. Examples include Tom Grazulis's Outbreak Intensity Score (OIS) for tornado outbreaks, and the Accumulated Cyclone Energy (ACE) index for tropical cyclone seasons. While these particular metrics do a reasonably good job of quantifying intensity, the scores themselves don't explicitly say much about rarity, and there are other high impact hazards that don't yet have a widely known scoring system (which includes straight-line wind events, hail events, wildfire outbreaks, and flooding events).
To address this shortcoming, I developed a scoring metric called the Relative Frequency Score (RFS), and this metric is intended to be used on large-scale weather events (e.g. tornado outbreaks) that are themselves composed of individual events (e.g. tornadoes). The calculation process goes as follows:
1. Using a large multi-decadal sample of data, divide each event up into categories of magnitude. For each category, count the number of events that fall into that category and then divide by the number of days in the examined timeframe. For tornadoes, this works out to be...
32,218 (E)F0's ÷ 27,028 days = 1.192 (E)F0's / day
23,782 (E)F1's ÷ 27,028 days = 0.8799 (E)F1's / day
9,767 (E)F2's ÷ 27,028 days = 0.3614 (E)F2's / day
2,585 (E)F3's ÷ 27,028 days = 0.09564 (E)F3's / day
587 (E)F4's ÷ 27,028 days = 0.02172 (E)F4's / day
59 (E)F5's ÷ 27,028 days = 0.002183 (E)F5's / day
Note that these values were obtained using the Storm Prediction Center's tornado database spreadsheet and examining the time period of 1950-2023 (74 years; 27,028 days).
2. For each individual event, calculate the result of 1 ÷ the daily ratio of that event's magnitude and add up the results. For a tornado outbreak with 13 (E)F0's, 8 (E)F1's, 4 (E)F2's and 3 (E)F3's, this would come out to be...
13 × (1 ÷ 1.192) + 8 × (1 ÷ 0.8799) + 4 × (1 ÷ 0.3614) + 3 × (1 ÷ 0.09564) = 62.434
So, for this hypothetical tornado outbreak example, the relative frequency score (RFS) would be 62.434, and the RFS would be something that is calculated for every tornado outbreak event.
However, there is still an important question that needs to be answered: What would qualify as a "significant" RFS value? Since Tom Grazulis's OIS metric uses a 7-tier categorization system, I decided to use a 7-tier system where the cutoff values for each tier were determined by calculating the RFS for each day with at least 1 tornado and then calculating the following percentiles:
Tier 7: 99.99th Percentile (Top 0.01 %)
Tier 6: 99.95th Percentile (Top 0.05 %)
Tier 5: 99.90th Percentile (Top 0.10 %)
Tier 4: 99.50th Percentile (Top 0.50 %)
Tier 3: 99.00th Percentile (Top 1.00 %)
Tier 2: 95.00th Percentile (Top 5.00 %)
Tier 1: 90.00th Percentile (Top 10.0 %)
Tier 0: Anything lower
Since these cutoff values are determined by percentiles, it is possible to generalize these tiers for any type of weather event. For tornadoes, the RFS cutoffs worked out to be (note that the cutoff values were truncated and not rounded):
Tier 7 (Super Outbreaks): RFS 2369+
Tier 6 (Extreme Outbreaks): RFS 826 - 2368
Tier 5 (Major Outbreaks): RFS 673 - 825
Tier 4 (Significant Outbreaks): RFS 239 - 672
Tier 3 (Moderate Outbreaks): RFS 131 - 238
Tier 2 (Minor Outbreaks): RFS 45 - 130
Tier 1 (Marginal Outbreaks): RFS 23 - 44
Tier 0 (Common Event): RFS < 23
In the case of tornado outbreak events specifically, the following events had RFS values that qualified as "super outbreaks":
- April 3, 1974: RFS = 4,707
- April 27, 2011: RFS = 2,778
And this result agrees with universal subjective evaluations and Tom Grazulis's OIS classifications.
For those that are interested, 5 tornado events produced an RFS value that qualified as an "extreme outbreak":
- March 13, 1990: RFS = 1,182
- May 15, 1968: RFS = 1,102
- May 25, 1955: RFS = 990
- April 11, 1965: RFS = 877
- May 31, 1985: RFS = 842
And, the "major outbreaks" (6 tornado events):
- April 26, 1991: RFS = 786
- April 2, 1982: RFS = 774
- April 3, 1956: RFS = 729
- May 3, 1999: RFS = 728
- June 16, 1992: RFS = 702
- May 24, 2011: RFS = 680
If you're interested in examining the RFS values for each individual tornado day from 1950-2023, a plain text file can be downloaded here. Note that each timestamp and its corresponding RFS score are separated by a colon (:). A ranked version is also available.
Again, the beautiful thing about this approach is that it can be generalized for any weather event that has a quantifiable or classifiable measurement and also has enough data to accurately estimate the frequency of each particular magnitude. Using local storm report (LSR) data from 2000-2024, straight-line wind reports were discretized into the following categories: "damage" (no wind speed provided), 50 knots (58 mph), 60 knots (69 mph), 70 knots (80 mph), 80 knots (92 mph), and 90 knots (103 mph). Hail reports were discretized into the following categories: 1.00"-1.49", 1.50"-1.99", 2.00"-2.99", 3.00"-3.99", 4.00"-4.99", and 5.00"+. The estimated frequencies for each are:
Straight-Line Winds:
Wind damage: 35.09 / day
Measured 50-59 knots (58-68 mph): 7.064 / day
Measured 60-69 knots (69-79 mph): 1.679 / day
Measured 70-79 knots (80-91 mph): 0.3885 / day
Measured 80-89 knots (92-102 mph): 0.05354 / day
Measured 90+ knots (103+ mph): 0.02428 / day
Tier 7 (Super): RFS 447+
Tier 6 (Extreme): RFS 295 - 446
Tier 5 (Major): RFS 230 - 294
Tier 4 (Significant): RFS 124 - 229
Tier 3 (Moderate): RFS 97 - 123
Tier 2 (Minor): RFS 44 - 96
Tier 1 (Marginal): RFS 23 - 43
Tier 0 (Common): RFS < 23
Hail:
1.00"-1.49": 11.63 / day
1.50"-1.99": 5.350 / day
2.00"-2.99": 1.615 / day
3.00"-3.99": 0.1617 / day
4.00"-4.99": 0.1130 / day
5.00"+: 0.004771 / day
Tier 7 (Super): RFS 825+
Tier 6 (Extreme): RFS 513 - 824
Tier 5 (Major): RFS 472 - 512
Tier 4 (Significant): RFS 243 - 471
Tier 3 (Moderate): RFS 105 - 242
Tier 2 (Minor): RFS 39 - 104
Tier 1 (Marginal): RFS 25 - 38
Tier 0 (Common): RFS < 25
Like with tornadoes, the aforementioned percentile cutoffs can be applied to all straight-line wind RFS values and all hail RFS values to classify them as "super events", "extreme events", "major events", "significant events", "moderate events", "minor events", "marginal events", and "common events". For those that are curious, the highest straight-line wind RFS value was 633 on August 10, 2020; and the highest hail RFS value was 892 on June 2, 2024 (when multiple 3.00"-6.00"+ hail reports were received).
The really elegant thing about the RFS calculation is that the normalization of each individual event magnitude provides a scale that makes it possible to compare one hazard to another. In other words, the RFS calculation allows us to compare the magnitude of a tornado event to a straight-line wind and/or a hail event. Relatively speaking, an RFS of 633 would imply a derecho event of this magnitude is about 7-8 times more common than the April 3rd, 1974 tornado outbreak event, and the June 2, 2024 hail event is considerably less common than the August 2020 derecho event. However, it should be noted that the true magnitude of wind and hail events can be skewed by population density bias, so these conclusions should be taken with a grain of salt. Still, the RFS values for any given hazard can be easily compared to the RFS values for any other hazard since the calculation is fully normalized.
Again, if you're interested, here are download links for the wind and hail RFS values with the same format as the tornado RFS text file:
- Straight-line winds: Raw Ranked
- Hail: Raw Ranked
Other numerical measurements that can have an RFS scale include (but are not limited to):
- Tornado Path Length
- Tornado Path Width
- Rain Gauge Measurements
- River and Lake Gauge Measurements
- Wildfire Acreage Burned
- Tropical Cyclone Minimum Pressure
- Tropical Cyclone Maximum Wind Speed
- Temperature Extremes
- Calculated Parameters (e.g. Dewpoint, Mixing Ratio, Convective Available Potential Energy, Storm Relative Helicity, etc.)
Methods may be differ in how individual event frequencies (probabilities) are estimated, but, as long as the same method is used for all measurements of all hazards, all resulting RFS values can be easily compared to each other without the need for any fancy conversions. And, any desired set of percentile cutoffs can be applied to any given set of RFS values to help classify "super events", "extreme events", all the way down to "marginal events" and "common events".
Another big advantage offered by the RFS calculation is its adaptability. If the frequencies (probabilities) for a particular event's magnitude change over time, the relative frequency can be re-calculated, and the RFS values and their classification cutoffs can easily be updated.
Update (April 15, 2025): The proposed calculation for relative frequency was updated to better represent the true rarity of an event, which should make comparing event types more of an "apples to apples" comparison.
Appendix: RFS Datasets
| Tornado Daily RFS: | Raw | Ranked |
| Tornado Monthly RFS: | Raw | Ranked |
| Tornado Yearly RFS: | Raw | Ranked |
| Wind Daily RFS: | Raw | Ranked |
| Wind Monthly RFS: | Raw | Ranked |
| Wind Yearly RFS: | Raw | Ranked |
| Hail Daily RFS: | Raw | Ranked |
| Hail Monthly RFS: | Raw | Ranked |
| Hail Yearly RFS: | Raw | Ranked |