# Climate Indices of Air Temperature

- Number of frost days and ice days
- Number of summer days and tropical nights
- Extreme temperature values during a specific period
- Exceeding specific limits (Percentile)
- Daily temperature range
- Heating degree day
- Warm and cold spell duration
- Growing season length

## Number of frost days and ice days

The **number of frost days (FD)** is the annual count of days when TN (daily minimum temperature) < 0^{o}C.

Let *TN _{ij}* be daily minimum temperature on day

*i*in year

*j*. Count the number of days where:

*TN _{ij}* < 0

^{o}C.

The **Number of icing days (ID)** is the annual count of days when TX (daily maximum temperature) < 0^{o}C.

Let *TX _{ij}*be daily maximum temperature on day

*i*in year

*j*. Count the number of days where:

*TX _{ij}* < 0

^{o}C.

## Number of summerdays and tropical nights

The **number of summer days (SU)** is the annual count of days when TX (daily maximum temperature) > 25^{o}C.

Let *TX _{ij}* be daily maximum temperature on day

*i*in year

*j*. Count the number of days where:

*TX _{ij}* > 25

^{o}C.

The **number of tropical nights (TR)** is the annual count of days when TN (daily minimum temperature) > 20^{o}C.

Let *TN _{ij}*be daily minimum temperature on day

*i*in year

*j*. Count the number of days where:

*TN _{ij}* > 20

^{o}C.

## Extreme temperature values during a specific period

Extremevalues are here defined as maxima and minima values of the maximum and minimum temperature. The following four cases are defined:

**Monthly maximum value of daily maximum temperature (TXx):**

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 (TNx):**

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 (TXn):**

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 (TNn):**

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}## Exceeding specific limits (Percentile)

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. (2004). The results include the **percentage of days with**

**Percentage of days when minimumtemperature TN < 10th percentile**** (TN10p):**

Let TN_{ij} be the daily minimum temperature on day *i* in period *j* and let TN_{in}10 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_{in}10.

**Percentage of days when TN > 90th percentile (TN90p):**

Let TN_{ij} be the daily minimum temperature on day *i* in period *j* and let TN_{in}90 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_{in}90.

**Percentage of days when TX < 10th percentile**** (TX10p):**

Let TX_{ij} be the daily maximum temperature on day *i* in period *j* and let TX_{in}10 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_{in}10

**Percentage of days when TX > 90th percentile (TX90p):**

Let TX_{ij} be the daily maximum temperature on day *i* in period *j* and let TX_{in}90 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_{in}90

## Daily temperature range

The **daily temperature range (DTR**) is defined as monthly mean difference between maximum temperature TX and minimum temperature TN: 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:

*DTR _{j} = *∑

^{I}

_{i}

*(TX*

_{ij}- TN_{ij}) / I## Heating degree days

The so called **heating degree days**** (HDD)** are a measure for the energy needed for heating an days at which the temperature falls below a defined limit. A typical value for this limit is an ambient temperature of 17°C. The related **heating degree days**** (HD17) **are the temperature sum of 17°C minus temperature of day with Tmeparature

T < 17°C.

## Warm and cold spell duration

Indices are defined for duration of cold and warm periods.

The **warm spell duration index (WSDI)** is defined as Annual count of days with at least 6 consecutive days when TX > 90^{th} percentile.

Let TX_{ij} be the daily maximum temperature on day *i* in period *j* and let TX_{in}90 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_{in}90.

The **cold spell duration index (CSDI)** is defined as annual count of days with at least 6 consecutive days when TN < 10^{th} percentile.

Let TN_{ij} be the daily maximum temperature on day *i* in period *j* and let TN_{in}10 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_{in}10

## Growing season length

The **Growing season length (GSL) **is the annual (1^{st} Jan to 31^{st} Dec in Northern Hemisphere (NH), 1^{st} July to 30^{th} June in Southern Hemisphere (SH)) count between first span of at least 6 days with daily mean temperature TG>5^{o}C and first span after July 1^{st} (Jan 1^{st} in SH) of 6 days with

TG < 5^{o}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*> 5

_{ij}^{o}C and the first occurrence after 1

^{st}July (1

^{st}January in SH) of at least 6 consecutive days with:

*TG _{ij}* < 5

^{o}C.

## References

This information is taken from:

http://etccdi.pacificclimate.org/list_27_indices.shtml

The following references are given there:

- Karl, T.R., N. Nicholls, and A. Ghazi, 1999: CLIVAR/GCOS/WMO workshop on indices and indicators for climate extremes: Workshop summary.
*Climatic Change*,**42**, 3-7. - Peterson, T.C., and Coauthors: 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. (pdf, not barrier-free)