Climpact allows you to calculate indices that are annual or monthly statistics of modelled or observed climate data. Here you can find descriptions and formulae for each of the indices.

### What are extremes indices?

The indices calculated by Climpact are annual statistics of weather. They answer questions like:

• TXx: How hot was the hottest day each year?
• TN10p: What fraction of nights each year fell below the 10th percentile of minimum temperature?
• Rx5day: How much rain fell during the rainiest 5-day stretch of the year?

As well as being calculated over the full year, many indices are available for a given month—the hottest day each January, for example.

Climpact offers indices derived from daily temperature and precipitation data. These indices are a standardised set recommended by the Expert Team on Sector-Specific Climate Indices (ET-SCI). The standardisation of these indices allows researchers to compare results across time periods, regions and source datasets.

#### Index definitions

##### 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.

##### 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 TXij be daily maximum 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).

##### 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 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.

##### 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 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.

##### 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 at least 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 at least 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 at least 30 °C

Number of days when TX ≥ 30 ≥C.

##### TX of at least 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 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).

##### 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 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 ≥ 10 mm

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

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

##### 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 RRijnn mm.

##### 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 precipitation amount on day i in period j, then:

$PRCPTOT j = ∑ i = 1 I RR i j$
##### 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.

### 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
• McKee, T.B., Doesken, N.J. & Kleist, J. 1993. The relationship of drought frequency and duration to time scales, Proceedings of the 8th Conference on Applied Climatology, 17, 1709–83.
• Nairn, J.R. & Fawcett, R.G. 2013. Defining heatwaves: heatwave defined as a heat-impact event servicing all community and business sectors in Australia, Centre for Australian Weather and Climate Research Technical Report #60. Download (PDF from cawcr.gov.au): https://www.cawcr.gov.au/technical-reports/CTR_060.pdf
• Perkins, S.E. & Alexander, L.V. 2013. On the Measurement of heatwaves, J. Climate, 26, 4500–17. doi: 10.1175/JCLI-D-12-00383.1
• 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
• Vicente-Serrano, S.M., Beguería, S. & López-Moreno, J.I. 2010. A Multiscalar Drought Index Sensitive to Global Warming: The Standardized Precipitation Evapotranspiration Index, J. Climate, 23, 1696–718. doi: 10.1175/2009JCLI2909.1
• WMO 2012. Standardized Precipitation Index User Guide (7 bis, avenue de la Paix — P.O. Box 2300 — CH 1211 Geneva 2 — Switzerland). Download (PDF from wamis.org): http://www.wamis.org/agm/pubs/SPI/WMO_1090_EN.pdf