The Climdex project offers a list of 27 climate extremes indices. These indices are annual or monthly statistics of modelled or observed climate data. Here you can find descriptions and formulae for each of the indices.

##### Number of frost days

Annual count of days when TN (daily minimum temperature) < 0°C. Let TNij be daily minimum temperature on day i in year j. Count the number of days where TNij < 0 °C.

##### Number of summer days

Annual count of days when TX (daily maximum temperature) > 25°C. Let TXij be daily minimum temperature on day i in year j. Count the number of days where TXij > 25 °C.

##### Number of icing days

Annual count of days when TX (daily maximum temperature) < 0 °C. Let TXijbe daily maximum temperature on day i in year j. Count the number of days where TXij < 0 °C.

##### Number of tropical nights

Annual count of days when TN (daily minimum temperature) > 20 °C. Let TNij be daily minimum temperature on day i in year j. Count the number of days where TNij > 20 °C.

##### Growing season length

Annual* count between the first span of at least 6 days with daily mean temperature TG >5 °C and the first span after July 1st (Jan 1st in SH) of 6 days with TG <5 °C.

Let TGij be daily mean temperature on day i in year j. Count the number of days between the first occurrence of at least 6 consecutive days with TGij > 5 °C and the first occurrence after 1st July (Jan 1st in SH) of at least 6 consecutive days with TGij < 5 °C.

* Annual means Jan 1st to Dec 31st in the Northern Hemisphere (NH); July 1st to June 30th in the Southern Hemisphere (SH).

##### Monthly maximum value of daily maximum temperature

Let TXx be the daily maximum temperatures in month k, period j. The maximum daily maximum temperature each month is then TXxkj = max(TXxkj).

##### Monthly maximum value of daily minimum temperature

Let TNx be the daily minimum temperatures in month k, period j. The maximum daily minimum temperature each month is then TNxkj = max(TNxkj).

##### Monthly minimum value of daily maximum temperature

Let TXn be the daily maximum temperatures in month k, period j. The minimum daily maximum temperature each month is then TXnkj = min(TXnkj)

##### Monthly minimum value of daily minimum temperature

Let TNn be the daily minimum temperatures in month k, period j. The minimum daily minimum temperature each month is then TNnkj=min(TNnkj)

##### Percentage of days when TN < 10th percentile

Let TNij be the daily minimum temperature on day i in period j and let TNin10 be the calendar day 10th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where: TNij < TNin10. To avoid possible inhomogeneity across the in-base and out-base periods, the calculation for the base period (1961-1990) requires the use of a bootstrap procedure. Details are described in Zhang et al. (2005).

##### Percentage of days when TX < 10th percentile

Let TXij be the daily maximum temperature on day i in period j and let TXin10 be the calendar day 10th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where TXij < TXin10. To avoid possible inhomogeneity across the in-base and out-base periods, the calculation for the base period (1961-1990) requires the use of a bootstrap processure. Details are described in Zhang et al. (2005).

##### Percentage of days when TN > 90th percentile

Let TNij be the daily minimum temperature on day i in period j and let TNin90 be the calendar day 90th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where TNij > TNin90. To avoid possible inhomogeneity across the in-base and out-base periods, the calculation for the base period (1961-1990) requires the use of a bootstrap processure. Details are described in Zhang et al. (2005)

##### Percentage of days when TX > 90th percentile

Let TXij be the daily maximum temperature on day i in period j and let TXin90 be the calendar day 90th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where TXij > TXin90. To avoid possible inhomogeneity across the in-base and out-base periods, the calculation for the base period (1961-1990) requires the use of a bootstrap processure. Details are described in Zhang et al. (2005).

##### Warm spell duration index: annual count of days with at least 6 consecutive days when TX > 90th percentile

Let TXij be the daily maximum temperature on day i in period j and let TXin90 be the calendar day 90th percentile centred on a 5-day window for the base period 1961-1990. Then the number of days per period is summed where, in intervals of at least 6 consecutive days, TXij > TXin90.

##### Cold spell duration index: annual count of days with at least 6 consecutive days when TN < 10th percentile

Let TNij be the daily maximum temperature on day i in period j and let TNin10 be the calendar day 10th percentile centred on a 5-day window for the base period 1961-1990. Then the number of days per period is summed where, in intervals of at least 6 consecutive days, TNij < TNin10.

##### Daily temperature range

Let TXij and TNij be the daily maximum and minimum temperature respectively on day i in period j. If i represents the number of days in j, then:

$DTR j = ∑ i = 1 I ( TX i j - TN i j ) I$
##### Monthly maximum 1-day precipitation

Let RRij be the daily precipitation amount on day i in period j. The maximum 1-day value for period j are Rx1dayj = max (RRij)

##### Monthly maximum consecutive 5-day precipitation

Let RRkj be the precipitation amount for the 5-day interval ending k, period j. Then maximum 5-day values for period j are Rx5dayj = max (RRkj)

##### Simple precipitation intensity index

Let RRwj be the daily precipitation amount on wet days, w (RR ≥ 1mm) in period j. If W represents number of wet days in j, then:

$SDII j = ∑ w = 1 W RR w j W$
##### Annual count of days when PRCP ≥ 10mm

Let RRij be the daily precipitation amount on day i in period j. Count the number of days where RRij ≥ 10mm

##### Annual count of days when PRCP ≥ 20mm

Let RRij be the daily precipitation amount on day i in period j. Count the number of days where RRij ≥ 20mm

##### Annual count of days when PRCP ≥ nn mm, where nn is a user-defined threshold

Let RRij be the daily precipitation amount on day i in period j. Count the number of days where RRij ≥ nnmm.

##### Maximum length of dry spell: maximum number of consecutive days with RR < 1mm

Let RRij be the daily precipitation amount on day i in period j. Count the largest number of consecutive days where RRij < 1mm.

##### Maximum length of wet spell: maximum number of consecutive days with RR ≥ 1mm

Let RRij be the daily precipitation amount on day i in period j. Count the largest number of consecutive days where RRij ≥ 1mm.

##### Annual total PRCP when RR > 95th percentile

Let RRwj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RRwn95 be the 95th percentile of precipitation on wet days in the 1961-1990 period. If W represents the number of wet days in the period, then:

$R95 p = ∑ w = 1 W RR w j where RR w j > RR w n 95$
##### Annual total PRCP when RR > 99th percentile

Let RRwj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RRwn99 be the 99th percentile of precipitation on wet days in the 1961-1990 period. If W represents the number of wet days in the period, then:

$R99 p = ∑ w = 1 W RR w j where RR w j > RR w n 99$
##### Annual total precipitation on wet days

Let RRij be the daily pre If i represents the number of days in j, then:

$PRCPTOT j = ∑ i = 1 I RR i j$

### References

• Karl, T.R., N. Nicholls, and A. Ghazi. 1999. CLIVAR/GCOS/WMO workshop on indices and indicators for climate extremes: Workshop summary, Weather and Climate Extremes, 42, 3-7. doi: 10.1007/978-94-015-9265-9_2
• Peterson, T.C., et al. 2001. Report on the Activities of the Working Group on Climate Change Detection and Related Rapporteurs 1998-2001, WMO, Rep. WCDMP-47, WMO-TD 1071, Geneve, Switzerland, 143pp. Download (PDF from clivar.org): Peterson et al. 2001 (PDF)
• Zhang, X., et al. 2005. Avoiding Inhomogeneity in Percentile-Based Indices of Temperature Extremes, J. Climate, 18, 1641-1651. doi: 10.1175/JCLI3366.1