The 7 indicators

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.

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 E3CI.

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:
E3CI 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 E3CI 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 95th 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 Tmaxi, 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(HSj) and the standard deviation σ(HSj)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 (HSj, 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 5th 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 Tmini, 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(CSj) and the standard deviation σ(CSj)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 (CSj, 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,SPI − 3j, 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 E3CI, to maintain the consistency with the other components, the opposite of SPI − 3j, k is taken.

BASELINE CALCULATION: On the reference period 1981-2010, for each month j, the 95th 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}_{}

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where Pi, j, k represents the daily precipitation (day i, month j, year k)

Over the reference period, for each month j, the mean value μ(EPj)and the standard deviation σ(EPj)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 95th percentile of daily maximum wind speed is computed, w95, 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 wmax, 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(LLIj)and the standard deviation σ(LLIj)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 SHiP4 (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(ESj) and the standard deviation σ(ESj) 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

https://www.spc.noaa.gov/exper/soundings/help/ship.html

BASELINE CALCULATION: On the reference period 1981-2010, for each month j, the cumulative value of the exceedance of the daily FWI5 indicator from the threshold associated with the high danger6 is computed. Subsequently, for each month j, the mean value μ(EFj) and the standard deviation σ(EFj) 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}_{}

STANDARDIZED ANOMALY COMPUTATION: Each month 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.