The **monitoring** of extreme meteorological events takes into account **seven specific dynamics**, each of which is allocated an indicator defined by studying the state of the art.

# The 7 indicators

## E3CI components

The assessment of the components exploits ERA5 (doi:10.24381/cds.adbb2d47), the fifth-generation atmospheric reanalysis produced by European Centre for Medium-Range Weather Forecasts [ECMWF] (https://youtu.be/FAGobvUGl24). ERA5 covers the entire Globe on regular latitude-longitude grids at 0.25° x 0.25° resolution from January 1950 to present. Hourly data on many atmospheric parameters together with estimates of uncertainty are available on Climate Data Store of Copernicus Climate Change Service [C3S]. ERA5 is updated daily with a latency of about 5 days permitting a constant update of the components forming E^{3}CI.

For each component, an indicator is used as proxy for several hazards. The reference value is computed on 1981-2010 time span while, at monthly basis, a Z-score respect to the reference value is computed.

**Disclaimer:**

**E ^{3}CI data is generated using Copernicus Climate Change Service information [2021]. Neither the European Commission nor ECMWF is responsible for any use that may be made of the Copernicus information or data it contains.**

The E^{3}CI components are defined as follows:

BASELINE CALCULATION: On the reference period 1981-2010, for each
calendar day, the maximum daily temperature of the surrounding five days
is considered. The 95^{th} percentile among the 150 values (5
days x 30 years) is computed and assumed as threshold. Then, the
exceedance value at monthly basis is computed as:

{HS}_{j,k} = \sum_{i = 1}^{n_{j}}{\max\left\lbrack 0;\ {T_{\max}}_{i,j,k} - {T_{\max}}_{95i,j} \right\rbrack}_{}

where *T*_{max}_{i, j, k} represents the maximum daily temperature (day *i*, month *j*, year *k*)

Over the reference period, for each month *j*, the mean value *μ*(*H**S*_{j}) and the standard deviation *σ*(*H**S*_{j})of
the cumulative exceedance values are calculated.

STANDARDIZED ANOMALY COMPUTATION: Each month *j* and year *k*, the cumulative value of daily
exceedance beyond the corresponding threshold (*H**S*_{j, k})
is transformed according to the formula:

{HS}_{Z - s,j,k} = \frac{{HS}_{j,k} - \mu\left( {HS}_{j} \right)}{\sigma\left( {HS}_{j} \right)}

[^{1}] PLEASE PAY ATTENTION, IN JULY 2023, THE FORMULATIONS ADOPTED FOR HEAT AND COLD STRESSES HAVE BEEN UPDATED TO MAKE THEM HOMOGENEOUS WITH THE OTHER COMPONENTS. INDEED, IN THIS WAY, ALL THE INDICATORS REPORT INFORMATION NOT ONLY ABOUT THE FREQUENCY BUT ALSO ABOUT THE MAGNITUDE OF EXTREME EVENTS.

[^{2}] Rousi, E., Kornhuber, K., Beobide-Arsuaga, G., Luo, F., & Coumou, D. (2022). Accelerated western European heatwave trends linked to more-persistent double jets over Eurasia. Nature Communications, 13(1). https://doi.org/10.1038/s41467-022-31432-y

BASELINE CALCULATION: On the reference period 1981-2010, for each
calendar day, the minimum daily temperature of the surrounding five days
is considered. The 5^{th} percentile among the 150 values (5
days x 30 years) is computed and assumed as threshold. Then, the
exceedance value at monthly basis is computed as:

{CS}_{j,k} = \sum_{i = 1}^{n_{j}}{\max\left\lbrack 0;\ {{abs(T}_{\min}}_{i,j,k} - {T_{\min}}_{95i,j}) \right\rbrack}_{}

where *T*_{min}_{i, j, k} represents the minimum daily temperature (day *i*, month *j*, year *k*)

Over the reference period, for each month *j*, the mean value *μ*(*C**S*_{j}) and the standard deviation *σ*(*C**S*_{j})of
the cumulative exceedance value are calculated.

STANDARDIZED ANOMALY COMPUTATION: Each month *j* and year *k*, the cumulative value of daily
exceedance beyond the corresponding threshold (*C**S*_{j, k})
is transformed according to the formula:

{CS}_{Z - s,j,k} = \frac{{CS}_{j,k} - \mu\left( j,\ T_{\min} \right)}{\sigma\left( j,\ T_{\min} \right)}

BASELINE CALCULATION: Standard Precipitation Index (SPI) ^{3} is assumed as reference indicator
considering 3 months as accumulation period for precipitation (SPI-3).
Over 1981-2010, for each month *j*, the 30 cumulated values are
fitted to a gamma probability distribution which is then transformed
into a normal distribution.

STANDARDIZED ANOMALY COMPUTATION: For each month *j* and year *k*,*S**P**I* − 3_{j, k} value represents units of standard deviation from the long-term
reference mean. According to the canonical approach, positive SPI
indicate values greater than median precipitation and negative values
indicate less than median precipitation. In E^{3}CI, to maintain
the consistency with the other components, the opposite of *S**P**I* − 3_{j, k} is taken.

BASELINE CALCULATION: On the reference period 1981-2010, for each
month *j*, the 95^{th} percentile of daily precipitation is computed. Then, the exceedance
value at monthly basis is computed as:

{EP}_{j,k} = \sum_{i = 1}^{n_{j}}{\max\left\lbrack 0;\ P_{i,j,k} - P_{95,j} \right\rbrack}_{}

<where *P*_{i, j, k} represents the daily precipitation (day *i*, month *j*, year *k*)

Over the reference period, for each month *j*, the mean value *μ*(*E**P*_{j})and
the standard deviation *σ*(*E**P*_{j})of
the exceedance values are calculated.

STANDARDIZED ANOMALY COMPUTATION: Each month *j* and year *k*, the exceedance value is
transformed according to the formula:

{EP}_{Z - s,j,k} = \frac{{EP}_{j,k} - \mu\left( {EP}_{j} \right)}{\sigma\left( {EP}_{j} \right)}

[^{3}]McKee, T.B., N.J. Doesken and J. Kleist. 1993. The relationship of drought frequency andduration to time scale. In: Proceedings of the Eighth Conference on Applied Climatology,Anaheim, California, 17–22 January 1993. Boston, American Meteorological Society, 179–184.Edwards, D.C. and T.B. McKee. 1997. Characteristics of 20th Century Drought in the UnitedStates at Multiple Time Scales. Climatology Report Number 97-2. Colorado State University, FortCollins.

BASELINE CALCULATION: On the reference period 1981-2010, for each
month *j*, the 95^{th} percentile of daily maximum wind speed is computed, *w*_{95, j}. Then, at
monthly basis, Local Loss Index (LLI, Donat et al., 2011;
doi:10.5194/nhess-11-1351-2011) is calculated as:

{LLI}_{j,k} = \sum_{i = 1}^{n_{j}}{\max\left\lbrack 0;\left( \frac{w_{max,ij,k}}{w_{95,j}} - 1 \right)^{3} \right\rbrack}

Where *w*_{max, ij, k} is the maximum wind speed computed considering mean hourly values for
day *i*, month *j*, year *k*. Over the reference period, for
each month *j*, the mean value *μ*(*L**L**I*_{j})and
the standard deviation *σ*(*L**L**I*_{j})are
calculated.

STANDARDIZED ANOMALY COMPUTATION: Each month *j* and year *k*, the exceedance value is
transformed according to the formula:

{LLI}_{Z - s,j,k} = \frac{{LLI}_{j,k} - \mu\left( {LLI}_{j} \right)}{\sigma\left( {LLI}_{j} \right)}

BASELINE CALCULATION: On the reference period 1981-2010, for each
month *j*, the cumulative value
of the exceedance of the daily SHiP^{4} (Significant Hail
Parameter) indicator value from the threshold (1)is computed The
threshold is fixed following indications provided by authoritative
agencies exploiting the index for operational purposes. Subsequently,
for each month *j*, the mean
value *μ*(*E**S*_{j}) and the standard deviation *σ*(*E**S*_{j}) of the exceedance value are calculated. Then, at monthly basis, the
exceedance of SHIP indicator values from the threshold value is
computed

{ES}_{j,k} = \sum_{i = 1}^{n_{j}}{\max\left\lbrack 0;\ S_{i,j,k} - 1 \right\rbrack}_{}

STANDARDIZED ANOMALY COMPUTATION: Each month *j* and year *k*, the exceedance value is
transformed according to the formula:

{ES}_{Z - s,j,k} = \frac{{ES}_{j,k} - \mu\left( {ES}_{j} \right)}{\sigma\left( {ES}_{j} \right)}

[^{4}] Here some reference to investigate the structure and the use of the indicator: Czernecki, B., Taszarek, M., Marosz, M., Półrolniczak, M., Kolendowicz, L., Wyszogrodzki, A., & Szturc, J. (2019). Application of machine learning to large hail prediction – The importance of radar reflectivity, lightning occurrence and convective parameters derived from ERA5. Atmospheric Research, 227, 249–262. https://doi.org/10.1016/j.atmosres.2019.05.010

BASELINE CALCULATION: On the reference period 1981-2010, for each
month *j*, the cumulative value
of the exceedance of the daily FWI^{5} indicator from the
threshold associated with the high danger^{6} is
computed. Subsequently, for each month *j*, the mean value *μ*(*E**F*_{j}) and the standard deviation *σ*(*E**F*_{j}) of the exceedance value are calculated. Then, at monthly basis, the
exceedance of SHIP indicator values from the threshold value is
computed:

{EF}_{j,k} = \sum_{i = 1}^{n_{j}}{\max\left\lbrack 0;\ F_{i,j,k} - 21.3 \right\rbrack}_{}

*j* and year *k*, the exceedance value is
transformed according to the formula:

{EF}_{Z - s,j,k} = \frac{{EF}_{j,k} - \mu\left( {EF}_{j} \right)}{\sigma\left( {EF}_{j} \right)}

[^{5}] Van Wagner, C. E. (1987). Development and structure of the Canadian Forest Fire Weather Index System. Vol. 35 (1987), 35, 35.

[^{6}] https://climate-adapt.eea.europa.eu/en/metadata/indicators/fire-weather-index-monthly-mean-1979-2019

For each month *j* and year *k*, the European Extreme Events
Climate Index is given by the mean of the different components.
Different and more effective formulations are currently under
development.