Indices dictionaries

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:

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

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

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.

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:

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

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:

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

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:

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