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

**i) HEAT STRESS **

BASELINE
CALCULATION: On the reference period 1981-2010, for each calendar day, the
maximum 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. For each month j, the
mean value \mu\left(j,\ T_{max}\right)\ and the
standard deviation \sigma\left(j,\ T_{max}\right)\ of the
number of days exceeding the corresponding threshold are calculated.

STANDARDIZED
ANOMALY COMPUTATION: Each month j and year k the number of days exceeding the corresponding threshold {HS}_{j,k} is standardized according to the formula:

{HS}_{std,j,k}=\frac{{HS}_{j,k}-\mu\left(j,\ T_{max}\right)}{\sigma\left(j,\ T_{max}\right)}

**ii) COLD STRESS **

BASELINE CALCULATION: On the reference period 1981-2010, for each
calendar day, the minimum 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. For each month j, the mean value \mu\left(j,\ T_{min}\right)\ and the standard deviation \sigma\left(j,\ T_{min}\right)\ of the number of days lower than the corresponding threshold are
calculated.

STANDARDIZED ANOMALY COMPUTATION: Each month j and year k the number of days lower than the corresponding threshold {CS}_{j,k} is standardized according to the formula:

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

**iii) DROUGHT**

BASELINE CALCULATION: Standard Precipitation Index (SPI) is assumed as reference
indicator considering 3 months as accumulation period of interest (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 {SPI-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 {SPI-3}_{j,k} is taken.

**iv) EXTREME PRECIPITATION **

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[0;\ P_{i,j,k}-P_{95,j}\right]}\ }

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 \mu\left(\ {EP}_j\right)\ and the standard deviation \sigma\left(\ {EP}_j\right)\ of the exceedance value are calculated.

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

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

**v) EXTREME WIND **

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[0;\left(\frac{w_{max,i,j,k}}{w_{95,j}}-1\right)^3\right]

Where w_{max,i,j,k} is the maximum wind speed computed considering mean hourly values. Over the reference period, for each month j, the mean value \mu\left(\ {LLI}_j\right)\ and the standard deviation \sigma\left({LLI}_j\right)\ are calculated.

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

{LLI}_{std,j,k}=\frac{{LLI}_{j,k}-\mu\left(\ {EP}_j\right)}{\sigma\left(\ {EP}_j\right)}

**vi) E**^{3}CI

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.