Number of frost days

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

TN below 2 °C

The number of days when TN < 2 °C.

TN below -2 °C

The number of days when TN < -2 °C.

TN below -20 °C

The number of days when TN < -20 °C.

Number of summer days

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

Number of icing days

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

Number of tropical nights

Annual count of days when TN (daily minimum temperature) > 20 °C. Let TN_ij be daily minimum temperature on day i in year j. Count the number of days where TN_ij > 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 1^st (Jan 1^st in SH) of 6 days with TG <5 °C.

Let TG_ij 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 TG_ij > 5 °C and the first occurrence after 1^st July (Jan 1^st in SH) of at least 6 consecutive days with TG_ij < 5 °C.

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

Monthly maximum value of daily maximum temperature

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

Monthly maximum value of daily minimum temperature

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

Monthly minimum value of daily maximum temperature

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

Monthly minimum value of daily minimum temperature

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

Mean TM

The mean daily mean temperature.

Mean TX

The mean daily maximum temperature.

Mean TN

The mean daily minimum temperature.

Percentage of days when TN < 10th percentile

Let TN_ij be the daily minimum temperature on day i in period j and let TN_in10 be the calendar day 10^th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where: TN_ij < TN_in10. 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 TX_ij be the daily maximum temperature on day i in period j and let TX_in10 be the calendar day 10^th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where TX_ij < TX_in10. 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 TN_ij be the daily minimum temperature on day i in period j and let TN_in90 be the calendar day 90^th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where TN_ij > 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)

Percentage of days when TX > 90th percentile

Let TX_ij be the daily maximum temperature on day i in period j and let TX_in90 be the calendar day 90^th percentile centred on a 5-day window for the base period 1961-1990. The percentage of time for the base period is determined where TX_ij > TX_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).

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

Let TX_ij be the daily maximum temperature on day i in period j and let TX_in90 be the calendar day 90^th 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, TX_ij > TX_in90.

User-defined WSDI

Annual number of days contributing to events where d or more consecutive days experience TX > 90th percentile.

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

Let TN_ij be the daily minimum temperature on day i in period j and let TN_in10 be the calendar day 10^th 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, TN_ij < TN_in10.

User-defined CSDI

Annual number of days contributing to events where d or more consecutive days experience TN < 10th percentile.

Percentage of days with temperature above the median

Percentage of days when TX > 50th percentile.

Very warm day threshold

The value of the 95th percentile of TX.

TM of greater than or equal to 5 °C

Number of days when TM (daily mean temperature) ≥ 5 °C.

TM of at least 5 °C

Number of days when TM (daily mean temperature) < 5 °C.

TM of greater than or equal to 10 °C

Number of days when TM (daily mean temperature) ≥ 10 °C.

TM of at least 10 °C

Number of days when TM (daily mean temperature) < 10 °C.

TX of greater than or equal to 30 °C

Number of days when TX ≥ 30 ≥C.

TX of greater than or equal to 35 °C

Number of days when TX ≥ 35 ≥C.

User-defined consecutive number of hot days and nights

Annual count of d consecutive days where both TX > 95th percentile and TN > 95th percentile, where 10 ≥ d ≥ 2.

Heating degree days

Annual sum of n - TM, where n is a user-defined, location-specific base temperature and TM < n. A measure of the energy demand needed to heat a building.

Cooling degree days

Annual sum of TM - n, where n is a user-defined, location-specific base temperature and TM > n. A measure of the energy demand needed to cool a building.

Growing degree days

Annual sum of TM - n, where n is a user-defined, location-specific base temperature and TM > n. A measure of heat accumulation used to predict plant growth rates.

Daily temperature range

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

$${\mathrm{DTR}}_j=\frac{\underset{i=1}{\overset{I}{\sum <!--\; \sum \; -->}}({\mathrm{TX}}_{ij}-{\mathrm{TN}}_{ij})}{I}$$

Monthly maximum 1-day precipitation

Let RR_ij be the daily precipitation amount on day i in period j. The maximum 1-day value for period j are Rx1day_j = max (RR_ij).

Monthly maximum consecutive 5-day precipitation

Let RR_kj be the precipitation amount for the 5-day interval ending _k, period j. Then maximum 5-day values for period j are Rx5day_j = max (RR_kj).

User-defined consecutive days PR amount

Maximum d-day PR total.

Standardised Precipitation Index

Measure of "drought" using the Standardised Precipitation Index on time scales of 3, 6 and 12 months. A drought measure specified as a precipitation deficit. See McKee et al. (1993) and the SPI User Guide (World Meteorological Organization 2012) for details.

Calculated using the SPEI package in R.

Standardised Precipitation Evapotranspiration Index

Measure of "drought" using the Standardised Precipitation Evapotranspiration Index on time scales of 3, 6 and 12 months. A drought measure specified using precipitation and evaporation. See Vicente-Serrano et al. (2010) for details.

Calculated using the SPEI package in R.

Simple precipitation intensity index

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

$${\mathrm{SDII}}_j=\frac{\underset{w=1}{\overset{W}{\sum <!--\; \sum \; -->}}{\mathrm{RR}}_{wj}}{W}$$

Annual count of days when PRCP ≥ 10mm

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

Annual count of days when PRCP ≥ 20 mm

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

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

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

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

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

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

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

Annual total PRCP when RR > 95th percentile

Let RR_wj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RR_wn95 be the 95^th percentile of precipitation on wet days in the 1961-1990 period. If W represents the number of wet days in the period, then:

$${\mathrm{R95}}_p=\underset{w=1}{\overset{W}{\sum <!--\; \sum \; -->}}{\mathrm{RR}}_{wj}\mathrm{where}{\mathrm{RR}}_{wj}>{\mathrm{RR}}_{wn}95$$

Annual total PRCP when RR > 99th percentile

Let RR_wj be the daily precipitation amount on a wet day w (RR ≥ 1.0mm) in period i and let RR_wn99 be the 99^th percentile of precipitation on wet days in the 1961-1990 period. If W represents the number of wet days in the period, then:

$${\mathrm{R99}}_p=\underset{w=1}{\overset{W}{\sum <!--\; \sum \; -->}}{\mathrm{RR}}_{wj}\mathrm{where}{\mathrm{RR}}_{wj}>{\mathrm{RR}}_{wn}99$$

Annual total precipitation on wet days

Let RR_ij be the daily precipitation amount on day i in period j, then:

$${\mathrm{PRCPTOT}}_j=\underset{i=1}{\overset{I}{\sum <!--\; \sum \; -->}}{\mathrm{RR}}_{ij}$$

User-defined consecutive number of cold days and nights

Annual count of d consecutive days where both TX < 5th percentile and TN < 5th percentile, where 10 ≥ d ≥ 2.

Heatwave number (HWN) as defined by either the Excess Heat Factor (EHF), 90th percentile of TX or the 90th percentile of TN

The number of individual heatwaves that occur each summer (Nov–Mar in southern hemisphere and May–Sep in northern hemisphere). A heatwave is defined as 3 or more days where either the EHF is positive, TX > 90th percentile of TX or where TN < 90th percentile of TN, where percentiles are calculated from base period specified by user.

See Perkins & Alexander (2013) for more details.

Heatwave frequency (HWF) as defined by either the Excess Heat Factor (EHF), 90th percentile of TX or the 90th percentile of TN

The number of days that contribute to heatwaves, as defined by HWN.

See Perkins & Alexander (2013) for more details.

Heatwave duration (HWD) as defined by either the Excess Heat Factor (EHF), 90th percentile of TX or the 90th percentile of TN

The length of the longest heatwave identified by HWN.

See Perkins & Alexander (2013) for more details.

Heatwave magnitude (HWM) as defined by either the Excess Heat Factor (EHF), 90th percentile of TX or the 90th percentile of TN

The mean temperature of all heatwaves identified by HWN.

See Perkins & Alexander (2013) for more details.

Heatwave amplitude (HWA) as defined by either the Excess Heat Factor (EHF), 90th percentile of TX or the 90th percentile of TN

The peak daily value in the hottest heatwave (defined as the heatwave with the highest HWM.

See Perkins & Alexander (2013) for more details.

Coldwave number (CWN) as defined by Excess Cold Factor (ECF)

The number of individual 'coldwaves' that occur each year.

See Nairn & Fawcett (2013) for more details.

Coldwave frequency (HWF) as defined by Excess Cold Factor (ECF)

The number of days that contribute to 'coldwaves', as defined by CWN_ECF.

See Nairn & Fawcett (2013) for more details.

Coldwave duration (CWD) as defined by Excess Cold Factor (ECF)

The length of the longest 'coldwave' identified by CWN_ECF.

See Nairn & Fawcett (2013) for more details.

Coldwave magnitude (CWM) as defined by Excess Cold Factor (ECF)

The mean temperature of all 'coldwaves' identified by CWN_ECF.

See Nairn & Fawcett (2013) for more details.

Coldwave amplitude (CWA) as defined by Excess Cold Factor (ECF)

The minimum daily value in the coldest heatwave (defined as the coldwave with the lowest EWM_ECF.

See Nairn & Fawcett (2013) for more details.