# Definitions of the core climate extreme indices

## There are 27 core climate extreme indicesFootnote 1

Index Definition Variable
Number of frost days (FD)

Annual count of days when daily minimum temperature is less than $0°C$.

Let TNij be daily minimum temperature on day i in year j.

Count the number of days where:

TN ij$<0°C$

minimum temperature
Number of summer days (SU)

Annual count of days when daily maximum temperature is greater than $25°C$.

Let TXij be daily maximum temperature on day i in year j.

Count the number of days where:

TX ij $>25°C$

maximum temperature
Number of icing days (ID) Annual count of days when daily maximum temperature is less than $0°C$.

Let TXij be daily maximum temperature on day i in year j.

Count the number of days where:

TXij $<0°C$

maximum temperature
Number of tropical nights (TR)

Annual count of days when daily minimum temperature is greater than $20°C$.

Let TNij be daily minimum temperature on day i in year j.

Count the number of days where:

TNij $>20°C$

minimum temperature
Growing season length (GSL)

Annual (January 1 to December 31 in Northern Hemisphere (NH), July 1 to June 30 in Southern Hemisphere (SH)) count between first span of at least 6 days with daily mean temperature greater than $5°C$ and first span after July 1 (January 1 in SH) of 6 days with daily mean temperature less than $5°C$.

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 July 1 (January 1 in SH) of at least 6 consecutive days with: TGij $<5°C$.

mean temperature
Monthly maximum value of daily maximum temperature (TXx)

Let TXx be the daily maximum temperatures in month k, period j.

The maximum daily maximum temperature each month is then:

TXxkj $=$ max(TXxkj)

maximum temperature
Monthly maximum value of daily minimum temperature (TNx)

Let TNx be the daily minimum temperatures in month k, period j.

The maximum daily minimum temperature each month is then:

TNxkj $=$ max(TNxkj)

maximum temperature
Monthly minimum value of daily maximum temperature (TXn)

Let TXn be the daily maximum temperatures in month k, period j.

The minimum daily maximum temperature each month is then:

TXnkj $=$ min(TXnkj)

minimum temperature
Monthly minimum value of daily minimum temperature (TNn)

Let TNn be the daily minimum temperatures in month k, period j.

The minimum daily minimum temperature each month is then:

TNnkj $=$ min(TNnkj)

minimum temperature
Percentage of days when daily minimum temperature is less than the 10th percentile (TN10p)

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).

minimum temperature
Percentage of days when daily maximum temperature is less than the 10th percentile (TX10p)

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 procedure. Details are described in Zhang et al. (2005).

maximum temperature
Percentage of days when daily minimum temperature is greater than the 90th percentile (TN90p)

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 $>TN$in90.

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).

minimum temperature
Percentage of days when daily maximum temperature is greater than the 90th percentile (TX90p)

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).

maximum temperature
Warm spell duration index (WSDI)

Annual count of days with at least 6 consecutive days when daily maximum temperature is greater than the 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

maximum temperature
Cold spell duration index (CSDI)

Annual count of days with at least 6 consecutive days when daily minimum temperature is less than the 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.

Then the number of days per period is summed where, in intervals of at least 6 consecutive days:

TNij $<$ TNin10

minimum temperature
Daily temperature range (DTR)

Monthly mean difference between daily maximum and minimum temperature

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:

DTRj$=\frac{\sum _{i=1}^{I}\left(\mathrm{TXij}-\mathrm{TNij}\right)}{I}$

minimum temperature

maximum temperature

Monthly maximum 1-day precipitation (Rx1day)

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)

precipitation
Monthly maximum consecutive 5-day precipitation (Rx5day)

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)

precipitation
Annual count of days when precipitation is greater than or equal to 10mm (R10mm)

Let RRij be the daily precipitation amount on day i in period j.

Count the number of days where:

RRij $\ge$ 10mm

precipitation
Simple precipitation intensity index (SDII)

Let RRwj be the daily precipitation amount on wet days, w (RR $\ge$ 1mm) in period j.

If W represents number of wet days in j, then:

$\mathrm{SDIIj}=\frac{\sum _{w=1}^{W}\mathrm{RRwj}}{W}$

precipitation
Annual count of days when precipitation is greater than or equal to 20mm (R20mm)

Let RRij be the daily precipitation amount on day i in period j.

Count the number of days where:

RRij $\ge$ 20mm

precipitation
Annual count of days when precipitation is greater than or equal to "nnmm", nn is a user defined threshold (Rnnmm)

Let RRij be the daily precipitation amount on day i in period j.

Count the number of days where:

RRij $\ge$ nnmm

precipitation
Maximum length of dry spell, maximum number of consecutive days with daily precipitation less than 1mm (CDD)

Let RRij be the daily precipitation amount on day i in period j.

Count the largest number of consecutive days where:

RRij $<$ 1mm

precipitation
Maximum length of wet spell, maximum number of consecutive days with daily precipitation greater than or equal to 1mm (CWD)

Let RRij be the daily precipitation amount on day i in period j.

Count the largest number of consecutive days where:

RRij $\ge$ 1mm

precipitation
Annual total precipitation when daily precipitation is greater than the 95th percentile (R95pTOT)

Let RRwj be the daily precipitation amount on a wet day, 'w', (RR $\ge$ 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:

R95pj = $\sum _{w=1}^{W}$RRwj where RRwj $>$RRwn95

precipitation
Annual total precipitation when daily precipitation is greater than the 99th percentile (R99pTOT)

Let RRwj be the daily precipitation amount on a wet day, 'w', (RR $\ge$ 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:

R99pj = $\sum _{w=1}^{W}$RRwj where RRwj $>$RRwn99

precipitation
Annual total precipitation in wet days (PRCPTOT)

Annual total precipitation in wet days:

Let RRij be the daily precipitation amount on day i in period j.

If I represents the number of days in j , then:

PRCPTOTj = $\sum _{i=1}^{I}$RRij

precipitation
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