Weather Extremes

Extreme Forecast Index (EFI) | Return Period of Extreme Events

Extreme Forecast Index (EFI) & Shift of Tails (SOT)

Potentially extreme weather can be identified with the powerful tools EFI and SOT. These indices provide ensemble-based measures of how likely and how extreme a weather event would be than usual, given as likelihood measure (not probability for a certain event).

efi: Extreme Forecast Index
sot: Shift Of Tails.

Both types of parameters are based on the Cumulative Distribution Function of the different models that make up the ensemble and refer to a certain time range over which they measure the tendency for extreme events. EFI values over 0.8 denote high likelihood for unusual conditions. SOT values signify their extremeness. Only for temperature, the shift of distribution tails is given for both the upper (default) and the lower tail (marked additionally).

Selection of time interval

These indices are queried together with a time range which they are valid for, i.e. t_2m_<range>_efi:idx. Date/time stamps are right aligned. Examples for time ranges:

Query EFI/SOT parameter with time range of 1 day (1d): https://api.meteomatics.com/2025-07-04T00:00:00Z--2025-07-09T00:00:00Z:P1D/t_2m_1d_efi:idx/47.4244818,9.3767173/html
```
validdate;t_2m_1d_efi:idx
2020-09-08T00:00:00Z;-0.306
2020-09-09T00:00:00Z;-0.062
2020-09-10T00:00:00Z;0.299
2020-09-11T00:00:00Z;0.323
2020-09-12T00:00:00Z;0.393
2020-09-13T00:00:00Z;0.480
```
Since the times are right aligned, the EFI index of 0.323 at 2025-07-07T00:00:00Z is valid for the period 2025-07-06T00:00:00Z--2025-07-07T00:00:00Z
Query EFI/SOT parameter with time range of 5 days (5d): https://api.meteomatics.com/2025-07-04T00:00:00Z--2025-07-09T00:00:00Z:P1D/t_2m_5d_efi:idx/47.4244818,9.3767173/html
```
validdate;t_2m_5d_efi:idx
2020-09-08T00:00:00Z;-0.083
2020-09-09T00:00:00Z;-0.021
2020-09-10T00:00:00Z;0.008
2020-09-11T00:00:00Z;-0.015
2020-09-12T00:00:00Z;0.069
2020-09-13T00:00:00Z;0.326
```
The EFI index of 0.326 at 2025-07-09T00:00:00Z is valid for the period 2025-07-04T00:00:00Z--2025-07-09T00:00:00Z

Parameters

```
convective_epot_avail_<range>_<type>:idx
```
Available ranges: 1d Available types: efi, sot

convective_epot_avail_shear_<range>_<type>:idx

Available ranges: 1d Available types: efi, sot

significant_wave_height_max_<range>_<type>:idx

Available ranges: 1d Available types: efi, sot

```
snowfall_<range>_<type>:idx
```
Available ranges: 1d Available types: efi, sot
```
t_2m_<range>_<type>:idx
```
Available ranges: 1d, 3d, 5d, 10d, 6w Available types: efi, sot, sot_q10
```
t_2m_max_<range>_<type>:idx
```
Available ranges: 1d Available types: efi, sot, sot_q10
```
t_2m_min_<range>_<type>:idx
```
Available ranges: 1d Available types: efi, sot, sot_q10
```
total_precipitation_accumulation_<range>_<type>:idx
```
Available ranges: 1d, 3d, 5d, 10d, 6w Available types: efi, sot, sot_q10
```
water_vapour_flux_<range>_<type>:idx
```
Available ranges: 1d, 3d, 5d, 10d Available types: efi, sot
```
wind_gust_10m_<range>_<type>:idx
```
Available ranges: 1d Available types: efi, sot
```
wind_speed_10m_<range>_<type>:idx
```
Available ranges: 1d, 3d, 5d, 10d Available types: efi, sot

Examples

Visualize how extreme the maximum wave height will potentially be during the day (right aligned). https://api.meteomatics.com/2025-07-04T12Z/significant_wave_height_max_1d_sot:idx/world:0.5,0.5/png

Create a time series how likely the temperature will be unusual, for a given pointhttps://api.meteomatics.com/2025-07-04T12ZP5D:P1D/t_2m_1d_efi:idx/32,157/csv

validdate;t_2m_1d_efi:idx
2020-07-23T12:00:00Z;0.915
2020-07-24T12:00:00Z;0.922
2020-07-25T12:00:00Z;0.910
2020-07-26T12:00:00Z;0.903
2020-07-27T12:00:00Z;0.885
2020-07-28T12:00:00Z;0.872

Return Period

The return period is an estimated average time between the occurrences of a defined event of a given severity for a selected area (e.g. extreme flooding event). The unit of the return period is years.

return_period:yrs

Example:<br/ >Defined event: Extremely high values of 24 hour accumulated precipitaton (1990 – 2020)

Return period: 10 years (mean of times between events)

Specifications

Parameter & time period

Identifier	Description	Example
`rp_source_parameter`	Parameter to be analyzed	`precip_24h:mm`
`rp_source_start_date`	Start time of investigated data	`1979-01-01Z`
`rp_source_end_date`	End time of investigated data	`2018-12-31Z`

Thresholds Daily values that are above or below a certain threshold can be ignored. The orientation of the threshold has to be defined as well. The setting of a threshold is optional.

`rp_threshold`	Value for a threshold	`None`, any numerical value (e.g. `50`), quantiles (e.g. `quantile0.25`)
`rp_threshold_orientation`	Defines the values that are kept	`below` (values above the threshold are set to invalid), `above` (values below the threshold are set to invalid)

Risk Window Relevant time window of the year that can be defined for the analysis. For example, if floodings are investigated, a plausible risk window would be May 1st until October 1st.

`rp_risk_window_aggregation`	Function used to accumulate/reduce daily valid values to single value per risk window	`min`, `mean`, `max`, `median`, `sum`
`rp_risk_window_start_day`	Start day of risk window	`1`
`rp_risk_window_start_month`	Start month of risk window	`5`
`rp_risk_window_end_day`	End day of risk window	`1`
`rp_risk_window_end_month`	End month of risk window	`10`

Extremes It has to be defined which orientation of extremes should be considered as severe conditions. The orientation can be either up, which takes large values into account, or down, which uses low values.

rp_extremes_orientation large (e.g. extreme rain) or low (e.g. frost) values indicate the rarest, most severe conditions up, down

Examples

Heavy rain event for a single coordinate: http://api.meteomatics.com/1979-01-01T00:00:00Z--2018-12-31T00:00:00Z:P12M/return_period:yrs/47.4,9.3/csv?rp_source_parameter=precip_24h:mm&rp_source_start_date=1979-01-01Z&rp_source_end_date=2018-12-31Z&rp_risk_window_aggregation=max&rp_risk_window_start_day=1&rp_risk_window_start_month=5&rp_risk_window_end_day=30&rp_risk_window_end_month=9&rp_extremes_orientation=up

rp_source_parameter=precip_24h:mm: parameter of interest is the 24 hour accumulated precipitation.
rp_risk_window_aggregation=max: aggregated single values for the risk window are calculated. Here, always the maximum values within the risk window is taken.
rp_extremes_orientation=up: the extremes orientation is set to up in order to consider high values as severe conditions.

 validdate;return_period:yrs
 1979-01-01T00:00:00Z;2.857
 1980-01-01T00:00:00Z;1.026
 1981-01-01T00:00:00Z;8.000
 1982-01-01T00:00:00Z;1.212
 1983-01-01T00:00:00Z;1.739
 1984-01-01T00:00:00Z;40.000
 1985-01-01T00:00:00Z;20.000
 1986-01-01T00:00:00Z;1.538
 1987-01-01T00:00:00Z;1.379
 1988-01-01T00:00:00Z;2.000
 1989-01-01T00:00:00Z;1.000
 ...

The output contains one value per year. For example, the value of 1.538 years in 1986 means that the maximum precipitation, which occurred in 1986 is expected to return every 1.538 years on average.

Dry conditions for a single coordinate: http://api.meteomatics.com/1979-01-01T00:00:00Z--2018-12-31T00:00:00Z:P12M/return_period:yrs/47.45,8.75/csv?rp_source_parameter=volumetric_soil_water_-15cm:m3m3&rp_source_start_date=1979-01-01Z&rp_source_end_date=2018-12-31Z&rp_risk_window_aggregation=min&rp_risk_window_start_day=1&rp_risk_window_start_month=1&rp_risk_window_end_day=31&rp_risk_window_end_month=12&rp_extremes_orientation=down

rp_source_parameter=volumetric_soil_water_-15cm:m3m3: parameter of interest is the soil moisture content in a depth of 15 cm.
rp_risk_window_aggregation=min: The minimum soil moisture values within the risk window are taken into account.
rp_extremes_orientation=down: the extremes orientation is set to down in order to consider low values as severe conditions.

 validdate;return_period:yrs
 1979-01-01T00:00:00Z;1.176
 1980-01-01T00:00:00Z;1.000
 ...
 2009-01-01T00:00:00Z;2.105
 2010-01-01T00:00:00Z;1.667
 2011-01-01T00:00:00Z;4.444
 2012-01-01T00:00:00Z;1.379
 2013-01-01T00:00:00Z;3.333
 2014-01-01T00:00:00Z;2.500
 2015-01-01T00:00:00Z;10.000
 2016-01-01T00:00:00Z;1.250
 2017-01-01T00:00:00Z;2.857
 2018-01-01T00:00:00Z;20.000

Dry conditions like in 2018 are expected to occur every 20 years on average.