Dictionnaire des indices

Cold indices

  • FD

    Frost days \((TN < 0°C)\) (Days)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\). Then counted is the number of days where:

    \(TN_{ij} < 0°C\)

    CFD

    Maximum number of consecutive frost days \((TN < 0°C)\) (Days)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\). Then counted is the largest number of consecutive days where:

    \(TN_{ij} < 0°C\)

    ID

    Ice days \((TX < 0°C)\) (Days)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\). Then counted is the number of days where:

    \(TX_{ij} < 0°C\)

    HD17

    Heating degree days (sum of \(17°C - TG)\) (\(°C\))

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\). Then the heating degree days are:

    \(HD17_{j} = \sum_{i=1}^{I}(17°C - TG_{ij})\)

    GSL

    Growing season length (days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\). Then counted is 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 July of at least 6 consecutive days with:

    \(TG_{ij} < 5°C\)

    TXn

    Minimum value of daily maximum temperature (°C)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\). Then the minimum of daily maximum temperature is:

    \(TXn_{j} = \min(TX_{ij})\)

    TNn

    Minimum value of daily minimum temperature (°C)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\). Then the minimum of daily minimum temperature is:

    \(TNn_{j} = \min(TN_{ij})\)

    TN10p

    Number of days with TN < 10th percentile of daily minimum temperature (cold nights) (days)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\) and let \(TN_{in}10\) be the calendar day 10th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where:

    \(TN_{ij} < TN_{in}10\)

    TG10p

    Number of days with TG < 10th percentile of daily mean temperature (cold days) (days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\) and let \(TG_{in}10\) be the calendar day 10th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where:

    \(TG_{ij} < TG_{in}10\)

    TX10p

    Number of days with TX < 10th percentile of daily maximum temperature (cold day-times) (days)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\) and let \(TX_{in}10\) be the calendar day 10th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where:

    \(TX_{ij} < TX_{in}10\)

    CSDI

    Cold-spell duration index (days)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\) and let \(TN_{in}10\) be the calendar day 10th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where, in intervals of at least 6 consecutive days:

    \(TN_{ij} < TN_{in}10\)

    GD4

    Growing Degree Days (°C)

    Let \(TG_{ij}\) be the daily mean temperature of day \(i\) of period \(j\). Then the growing degree days are:

    \(GD4_{j} = \sum_{i=1}^{I}(TG_{ij} -4 | TG_{ij} > 4°C) \)

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Compound indices

  • HI

    Huglin Index (grape growth)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) and let \(TX_{i}\) be the daily maximum temperature at day \(i\) of the period 1 April to 30 September. Then the Huglin Index is:

    \(HI = \sum_{1/4}^{30/9}{(TG_{i} - 10) + (TX_{i} - 10) \over 2} K \)

    where \(K\) is a coefficient for day length. See here for details.

    BEDD

    Biologically Effective Degree Days

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) and let \(TX_{i}\) be the daily maximum temperature at day \(i\) of the period 1 April to 30 September. Then BEDD is a growing degree days measure for grapes:

    \(BEDD = \sum_{1/4}^{30/9}{ \min{ ( (\max{ [ ({ TX_{i} + TN_{i} \over 2}) - b, 0] } ),9) }} \)

    where \(b\) is 10. See here for details.

    CD

    Days with \(TG \lt\) 25th percentile of daily mean temperature and \(RR \lt\) 25th percentile of daily precipitation amount (cold/dry days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\) and let \(TG_{in}25\) be the calendar day 25th percentile calculated for a 5-day window centred on each calendar day in the 1961-1990 period. Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1.0\) mm) of period \(j\) and let \(RR_{wn}25\) be the 25th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \(TG_{ij} < TG_{in}25\) and \(RR_{wj} < RR_{wn}25 \)

    CW

    Days with \(TG \lt\) 25th percentile of daily mean temperature and \(RR \gt\) 75th percentile of daily precipitation amount (cold/wet days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\) and let \(TG_{in}25\) be the calendar day 25th percentile calculated for a 5-day window centred on each calendar day in the 1961-1990 period. Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1.0\) mm) of period \(j\) and let \(RR_{wn}75\) be the 75th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \(TG_{ij} < TG_{in}25\) and \(RR_{wj} > RR_{wn}75 \)

    WD

    Days with \(TG \gt\) 75th percentile of daily mean temperature and \(RR \lt\) 25th percentile of daily precipitation amount (warm/dry days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\) and let \(TG_{in}75\) be the calendar day 75th percentile calculated for a 5-day window centred on each calendar day in the 1961-1990 period. Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1.0\) mm) of period \(j\) and let \(RR_{wn}25\) be the 25th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \(TG_{ij} > TG_{in}75\) and \(RR_{wj} < RR_{wn}25 \)

    WW

    Days with \(TG \gt\) 75th percentile of daily mean temperature and \(RR \gt\) 75th percentile of daily precipitation amount (warm/wet days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\) and let \(TG_{in}75\) be the calendar day 75th percentile calculated for a 5-day window centred on each calendar day in the 1961-1990 period. Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1.0\) mm) of period \(j\) and let \(RR_{wn}75\) be the 75th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \(TG_{ij} > TG_{in}75\) and \(RR_{wj} > RR_{wn}75 \)

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Drought indices

  • CDD

    Maximum number of consecutive dry days \((RR < 1 mm)\) (Days)

    Let \(RR_{ij}\) be the daily precipitation amount at day \(i\) of period \(j\). Then counted is the largest number of consecutive days where:

    \(RR_{ij} < 1 mm\)

    SPI3

    3-Month Standardized Precipitation Index

    SPI is a probability index based on precipitation. It is designed to be a spatially invariant indicator of drought. SPI3 refers to precipitation in the previous 3-month period (\(+\) indicates wet; \(-\) indicates dry).
    See for details and the algorithm: Guttman, N.B. (1999) Accepting the standardized precipitation index: A calculation algorithm, J. Amer. Water Resources Assoc., 35 (2): 311-322.

    SPI6

    6-Month Standardized Precipitation Index

    SPI is a probability index based on precipitation. It is designed to be a spatially invariant indicator of drought. SPI6 refers to precipitation in the previous 6-month period (\(+\) indicates wet; \(-\) indicates dry).
    See for details and the algorithm: Guttman, N.B. (1999) Accepting the standardized precipitation index: A calculation algorithm, J. Amer. Water Resources Assoc., 35 (2): 311-322.

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Heat indices

  • SU

    Summer days \((TX > 25°C)\) (days)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\). Then counted is the number of days where:

    \(TX_{ij} > 25°C\)

    CSU

    Maximum number of consecutive summer days \((TX > 25°C)\) (Days)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\). Then counted is the largest number of consecutive days where:

    \(TX_{ij} > 25°C\)

    TR

    Tropical nights \((TN > 20°C)\) (days)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\). Then counted is the number of days where:

    \(TN_{ij} > 20°C\)

    TXx

    Maximum value of daily maximum temperature (°C)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\). Then the maximum of daily maximum temperature is:

    \(TXx_{j} = \max(TX_{ij})\)

    TNx

    Maximum value of daily minimum temperature (°C)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\). Then the maximum of daily minimum temperature is:

    \(TNx_{j} = \max(TN_{ij})\)

    TN90p

    Number of days with TN > 90th percentile of daily minimum temperature (warm nights) (days)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\) and let \(TN_{in}90\) be the calendar day 90th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where:

    \(TN_{ij} > TN_{in}90\)

    TG90p

    Number of days with TG > 90th percentile of daily mean temperature (warm days) (days)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\) and let \(TG_{in}90\) be the calendar day 90th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where:

    \(TG_{ij} > TG_{in}90\)

    TX90p

    Number of days with TX > 90th percentile of daily mean temperature (warm day-times) (days)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\) and let \(TX_{in}90\) be the calendar day 90th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where:

    \(TX_{ij} > TX_{in}90\)

    WSDI

    Warm-spell duration index (days)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\) and let \(TX_{in}10\) be the calendar day 90th percentile calculated for a 5 day window centred on each calendar day in the 1961-1990 period. Then counted is the number of days where, in intervals of at least 6 consecutive days:

    \(TX_{ij} > TX_{in}90\)

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Rain indices

  • RX1day

    Highest 1-day precipitation amount (mm)

    Let \(RR_{ij}\) be the daily precipitation amount at day \(i\) of period \(j\). Then the maximum 1-day value is:

    \(RX1day_{j} = \max{RR_{ij}}\)

    RX5day

    Highest 5-day precipitation amount (mm)

    Let \(RR_{kj}\) be the precipitation amount for the five-day interval \(k\) of period \(j\), where \(k\) is defined by the last day. Then the maximum 5-day value is:

    \(RX5day_{j} = \max{RR_{kj}}\)

    SDII

    Simple daily intensity index (mm/wet day)

    Let \(RR_{wj}\) be the daily precipitation amount for wet day \(w\) (\(RR \ge 1\) mm) of period \(j\). Then the mean precipitation amount at wet days is given by:

    \(SDII_{j} = \sum_{w=1}^{W}{RR_{wj}}/W\)

    RR

    Precipitation sum (mm)

    Let \(RR_{ij}\) be the daily precipitation amount for day \(i\) of period \(j\). Then sum values are given by:

    \(RR_{j} = \sum_{i=1}^{I}RR_{ij}\)

    RR1

    Wet days (\(RR \ge 1\) mm) (days)

    Let \(RR_{ij}\) be the daily precipitation amount for day \(i\) of period \(j\). Then counted is the number of days where:

    \(RR_{ij} \ge 1\ mm\)

    R10mm

    Heavy precipitation days (\(RR \ge 10\) mm) (days)

    Let \(RR_{ij}\) be the daily precipitation amount for day \(i\) of period \(j\). Then counted is the number of days where:

    \(RR_{ij} \ge 10\ mm\)

    R20mm

    Very heavy precipitation days (\(RR \ge 20\) mm) (days)

    Let \(RR_{ij}\) be the daily precipitation amount for day \(i\) of period \(j\). Then counted is the number of days where:

    \(RR_{ij} \ge 20\ mm\)

    CWD

    Maximum number of consecutive wet days (\(RR \ge 1\) mm) (days)

    Let \(RR_{ij}\) be the daily precipitation amount for day \(i\) of period \(j\). Then counted is the largest number of consecutive days where:

    \(RR_{ij} \ge 1\ mm\)

    R75pTOT

    Precipitation fraction due to moderate wet days (\(RR > 75th\) percentile) (%)

    Let \(RR_{j}\) be the sum of daily precipitation amount for period \(j\) and let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\) and \(RR_{wn}75\) the 75th percentile of precipitation at wet days in the 1961-1990 period. Then the fraction is determined as:

    \(R75pTOT_{j} = 100 * {{\sum_{w=1}^{W}RR_{wj},\ where\ RR_{wj} > RR_{wn}75} \over {RR_{j}}} \)

    R95pTOT

    Precipitation fraction due to very wet days (\(RR > 95th\) percentile) (%)

    Let \(RR_{j}\) be the sum of daily precipitation amount for period \(j\) and let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\) and \(RR_{wn}95\) the 95th percentile of precipitation at wet days in the 1961-1990 period. Then the fraction is determined as:

    \(R95pTOT_{j} = 100 * {{\sum_{w=1}^{W}RR_{wj},\ where\ RR_{wj} > RR_{wn}95} \over {RR_{j}}} \)

    R99pTOT

    Precipitation fraction due to extremely wet days (\(RR > 99th\) percentile) (%)

    Let \(RR_{j}\) be the sum of daily precipitation amount for period \(j\) and let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\) and \(RR_{wn}99\) the 99th percentile of precipitation at wet days in the 1961-1990 period. Then the fraction is determined as:

    \(R99pTOT_{j} = 100 * {{\sum_{w=1}^{W}RR_{wj},\ where\ RR_{wj} > RR_{wn}99} \over {RR_{j}}} \)

    R75p

    Days with (\(RR > 75th\) percentile of daily amounts (moderate wet days) (days)

    Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\) and \(RR_{wn}75\) the 75th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \( RR_{wj} > RR_{wn}75\)

    R95p

    Days with (\(RR > 95th\) percentile of daily amounts (very wet days) (days)

    Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\) and \(RR_{wn}95\) the 95th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \(RR_{wj} > RR_{wn}95 \)

    R99p

    Days with (\(RR > 99th\) percentile of daily amounts (extremely wet days) (days)

    Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\) and \(RR_{wn}99\) the 99th percentile of precipitation at wet days in the 1961-1990 period. Then counted is the number of days where:

    \(RR_{wj} > RR_{wn}99 \)

    PRCPTOT

    Total precipitation in wet days (\(RR > 1\) mm) (mm)

    Let \(RR_{wj}\) be the daily precipitation amount at wet day \(w\) (\(RR \ge 1\) mm) of period \(j\). Then the total is determined as:

    \(PRCPTOT_{j} = \sum_{w=1}^{W}RR_{wj} \)

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Temperature indices

  • TN

    Mean of daily minimum temperature (°C)

    Let \(TN_{ij}\) be the daily minimum temperature at day \(i\) of period \(j\). Then mean values in period \(j\) are given by:

    \(TN_{j} = {{\sum_{i=1}^{I}{ TN_{ij}} / I }}\)

    TG

    Mean of daily mean temperature (°C)

    Let \(TG_{ij}\) be the daily mean temperature at day \(i\) of period \(j\). Then mean values in period \(j\) are given by:

    \(TG_{j} = {{\sum_{i=1}^{I}{ TG_{ij}} / I }}\)

    TX

    Mean of daily maximum temperature (°C)

    Let \(TX_{ij}\) be the daily maximum temperature at day \(i\) of period \(j\). Then mean values in period \(j\) are given by:

    \(TX_{j} = {{\sum_{i=1}^{I}{ TX_{ij}} / I }}\)

    DTR

    Mean of diurnal temperature range (°C)

    Let \(TX_{ij}\) and \(TN_{ij}\) be the daily maximum and minimum temperature at day \(i\) of period \(j\). Then the mean diurnal temperature range in period \(j\) is:

    \(DTR_{j} = {{\sum_{i=1}^{I}{ | ( TX_{ij} - TN_{ij}) | } / I}}\)

    vDTR

    Mean absolute day-to-day difference in DTR (°C)

    Let \(TX_{ij}\) and \(TN_{ij}\) be the daily maximum and minimum temperature at day \(i\) of period \(j\). Then calculated is the absolute day-to-day difference in period \(j\):

    \(vDTR_{j} = {{\sum_{i=1}^{I}{ | ( TX_{ij} - TN_{ij}) - ( TX_{i-1,j} - TN_{i-1,j})} | / I}}\)

    ETR

    Intra-period extreme temperature range (°C)

    Let \(TX_{ij}\) and \(TN_{ij}\) be the daily maximum and minimum temperature at day \(i\) of period \(j\). Then the extreme temperature range in period \(j\) is:

    \(ETR_{j} = \max{(TX_{ij})} - \min{(TN_{ij})} \)

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