57
where r k is the autocorrelation function of time series x t at lag k, x t is observed
data flow series, x is the mean of time series (x t ), N denote the total length of x t
time-series, k is the maximum lag.
Since the test is two-tailed, the alternative hypothesis is that the true r k must be
other than zero; however, it may be positive or negative. The data of the time series
are considered as serially correlated if r k falls between the bigger and smaller margins of confidence interval (Anderson 1954); otherwise the time series data are supposed to be serially independent.
3.3.2 Precipitation Concentration Index
The precipitation concentration index (Oliver 1980; Michiels et al. 1992) recommended as an indicator of precipitation attentiveness which is computed according
to the following formula:
PCI
P
P
j
j
j
j
annual
¦
¦
u
1
12
2
1
12
2
100
(3.2)
where PCI denotes the precipitation concentration index, P j represents the monthly
precipitation in month j.
However, in the year of 1980, Oliver recommended that the distribution of precipitation would be uniform (precipitation concentration is low) while the values of
PCI are <10%; PCI values range from 11% to 15% symbolize a moderate precipitation concentration; PCI values from 16% to 20% denote irregular distribution and
distribution would be strongly irregular (high precipitation concentration) when the
PCI values are more than 20%.
3.3.3 Rainfall Seasonality Index (RSI)
Walsh and Lawler (1981) recommended the rainfall seasonality index (SI) to compute the degree of variability in monthly precipitation over the year as follows:
SI R
X
R
n
n
¦
1
12
12
1
(3.3)
where X n represents the total monthly precipitation, and R represents the total annual
precipitation.
Theoretically, the rainfall seasonality index (SI) can vary from zero (if equal
precipitation occurs in all months) to 1.83 (if total precipitation occurs in an individual month). The maximum values of SI specify an extreme variation of
3 Rainfall Insight in Bangladesh and India: Climate Change and Environmental…
where r k is the autocorrelation function of time series x t at lag k, x t is observed
data flow series, x is the mean of time series (x t ), N denote the total length of x t
time-series, k is the maximum lag.
Since the test is two-tailed, the alternative hypothesis is that the true r k must be
other than zero; however, it may be positive or negative. The data of the time series
are considered as serially correlated if r k falls between the bigger and smaller margins of confidence interval (Anderson 1954); otherwise the time series data are supposed to be serially independent.
3.3.2 Precipitation Concentration Index
The precipitation concentration index (Oliver 1980; Michiels et al. 1992) recommended as an indicator of precipitation attentiveness which is computed according
to the following formula:
PCI
P
P
j
j
j
j
annual
¦
¦
u
1
12
2
1
12
2
100
(3.2)
where PCI denotes the precipitation concentration index, P j represents the monthly
precipitation in month j.
However, in the year of 1980, Oliver recommended that the distribution of precipitation would be uniform (precipitation concentration is low) while the values of
PCI are <10%; PCI values range from 11% to 15% symbolize a moderate precipitation concentration; PCI values from 16% to 20% denote irregular distribution and
distribution would be strongly irregular (high precipitation concentration) when the
PCI values are more than 20%.
3.3.3 Rainfall Seasonality Index (RSI)
Walsh and Lawler (1981) recommended the rainfall seasonality index (SI) to compute the degree of variability in monthly precipitation over the year as follows:
SI R
X
R
n
n
¦
1
12
12
1
(3.3)
where X n represents the total monthly precipitation, and R represents the total annual
precipitation.
Theoretically, the rainfall seasonality index (SI) can vary from zero (if equal
precipitation occurs in all months) to 1.83 (if total precipitation occurs in an individual month). The maximum values of SI specify an extreme variation of
3 Rainfall Insight in Bangladesh and India: Climate Change and Environmental…