Extreme storms

To calculate Extreme storms Risk, we use the following variables [Copernicus Climate Data Store (CDS)]:

• daily air temperature: daily mean air temperature (°C), at various altitudes.
• daily relative humidity: daily mean air relative humidity, at various altitudes.
• daily eastward wind: daily mean eastward component of wind speed (m/s), at various altitudes.
• daily northward wind: daily mean northward component of wind speed (m/s), at various altitudes.

Extreme Storm Risk assesses potential for development of severe convective phenomena, such as violent thunderstorms, large hailstones and tornadoes. Risk is not based on a single variable, but on identification of days when three fundamental atmospheric 'ingredients' for these storm formation occur simultaneously.

The three key calculated indicators are:

• Wind Shear (Wind Variation with Height): Difference in wind speed and direction between low and high atmosphere. High Wind Shear is crucial because it allows thunderstorms to organize, rotate (forming supercells) and last longer.
• CAPE (Convective Available Potential Energy): Measures atmospheric instability, representing 'fuel' available to a storm. High CAPE values indicate that an ascending air mass will accelerate violently upward, generating strong currents and powerful thunderstorms.
• CIN (Convective Inhibition): Represents a stable air layer near ground acting as a 'lid', hindering thunderstorm formation. For a storm to develop, this layer must be weak or absent (low or very negative CIN values).

Wind Shear is calculated from eastward wind (u) and daily northward wind (v) data, evaluated at altitudes of 1000hPa (about 100m, 'low') and 500hPa (about 5.5km, 'up'), using the following formula:

$\text{Wind Shear} = \sqrt{\Delta u^2 + \Delta v^2}$ where $\Delta u = u_{\text{up}} - u_{\text{low}}$ and $\Delta v = v_{\text{up}} - v_{\text{low}}$.

CAPE and CIN indicators are calculated using the metpy library, from air temperature and relative humidity data at various altitudes.

A 'Day with Severe Potential' is identified when all three indicators simultaneously exceed their respective critical thresholds: $\text{Wind Shear} > 18 \text{ m/s}$, $\text{CAPE} > 1000 \text{ J/kg}$ and $\text{CIN} < -50 \text{ J/kg}$. Annual risk level is determined by total count of these days (N_severe) during the year.

The methodology described for assessing 'Extreme Storm Risk' is a direct and scientifically rigorous application of the 'ingredients-based approach', which is the foundation of modern severe thunderstorm forecasting.

This method is considered the reference standard because it doesn't limit itself to a single parameter, but assesses coexistence of atmospheric conditions necessary for genesis of organized and severe convective phenomena.

The idea of decomposing severe thunderstorm forecasting into key ingredients (instability, moisture, lifting and wind shear) was formalized and popularized by studies that transformed operational meteorology.

• Flash Flood Forecasting: An Ingredients-Based Methodology This is one of the articles that consolidated the ingredients-based approach for all types of convective event forecasts. It explains that to have a severe event, a single ingredient (e.g., high instability) is not enough, but their overlap in space and time is necessary. Our methodology, which requires simultaneous presence of CAPE, low CIN and Shear, is the application of this fundamental principle.

The three indicators used and relative thresholds are standard parameters widely documented in scientific literature and used daily by meteorological forecasting centers, such as the US Storm Prediction Center (SPC), which is a world authority in this matter.

• A Baseline Climatology of Sounding-Derived Supercell andTornado Forecast Parameters This foundational study analyzed thousands of atmospheric profiles to identify CAPE and Wind Shear values most commonly associated with supercell thunderstorms (the most dangerous type). It demonstrated that Deep Layer Shear (0-6 km) values of 18-20 m/s (35-40 knots) and CAPE above 1000 J/kg are typical of environments producing supercells and tornadoes. Our thresholds are therefore supported by this study.
• Storm Prediction Center (SPC) SPC provides operational guidelines for its meteorologists specifying 'rules of thumb' for severe thunderstorm forecasting. These guides confirm that:
• CAPE > 1000 J/kg indicates moderate instability, sufficient for robust thunderstorms.
• Wind Shear (0-6 km) > 18 m/s (~35 knots) is a key threshold for organizing thunderstorms into more complex and lasting systems (supercells).
• CIN < -50 J/kg (or values near zero) indicates 'lid' is weak and easily overcome by updrafts, allowing convection initiation.

The approach of counting number of days per year when conditions favorable to severe thunderstorms occur simultaneously is the standard method used in climatological research to study how extreme storm risk might change in the future.

• The spatial distribution of severe thunderstorm and tornado environments from global reanalysis data This is a pioneering and among the most cited articles in the field, where authors follow exactly the methodology we describe: they used global reanalysis data to count number of days per year when CAPE and Wind Shear values simultaneously exceeded critical thresholds. Thus, they created the first global climatological map of 'favorable environments' for severe thunderstorms. More recent studies use the same method (counting days $N_{\text{severe}}$) applying it to climate models to project how extreme storm risk will change in a warmer world. In conclusion, our methodology reflects state of the art. It is an application of ingredients-based paradigm (Doswell et al.), uses indicators and thresholds validated by research and operational practice (Rasmussen & Blanchard, SPC), and assesses annual risk with a standard method in severe phenomena climatology (Brooks et al.).