Hydrological Sciences-Journal- des Sciences Hydrologiques, 43(6) December 1998
345
Trends and persistence in precipitation in the
Ganges, Brahmaputra and Meghna river basins
M. Q. MIRZA, R. A. WARRICK, N. J. ERICKSEN &
G. J. KENNY
International Global Change Institute (IGCI) University of Waikato, Private Bag 3105,
Hamilton, New Zealand
Abstract The Ganges, Brahmaputra and Meghna (GBM) river basins occupy about
1.75 x 106 km2 of the Himalayan region. More than half a billion people in Nepal,
India, Bhutan and Bangladesh are directly or indirectly dependent on the water
resources of the GBM rivers. These river basins are characterized by diversified
climatic patterns. Analyses of trends and persistence in precipitation over these river
basins are necessary for sound water resources planning. Time series of annual
precipitation for each of the 16 meteorological subdivisions covering the three river
basins were examined for trends using the Mann-Kendall rank statistic, Student's f-test
and regression analysis, and for persistence using first order autocorrelation analysis.
Results indicate that precipitation in the Ganges basin is by-and-large stable.
Precipitation in one subdivision in the Brahmaputra basin shows a decreasing trend and
another shows an increasing trend. One of the three subdivisions in the Meghna basin
shows a decreasing trend while another shows an increasing trend. Markovian
persistence is not present in the precipitation series in the Ganges basin but it is present
in two common subdivisions in the Brahmaputra and Meghna basins.
Tendances et persistance des précipitations des bassins des fleuves
Gange, Brahmapoutre et Meghna
Résumé Les bassins des fleuves Gange, Brahmapoutre et Meghna (GBM) occupent
une surface d'à peu près 1.75 x 106 de km2 dans la région Himalayenne. Plus d'un
demi milliard de personnes au Népal, en Inde, au Bhoutan et au Bangladesh dépendent
directement ou indirectement des ressources d'eau des fleuves GBM. Les bassins de
ces fleuves sont caractérisés par des contextes climatiques variés. Des analyses de
tendances et de persistance des précipitations de ces bassins se sont révélées
nécessaires en vue de réaliser une planification efficace des ressources en eau. Nous
avons étudié les séries chronologiques des précipitations annuelles de chacune des
seize sous-divisions météorologiques couvrant les trois bassins fluviaux en utilisant la
statistique de Mann-Kendall, le test t de Student et l'analyse de régression ainsi que
l'auto-corrélation du premier ordre pour les problèmes de persistance. Les résultats
indiquent que les précipitations du bassin du Gange sont relativement stables. Les
précipitations de l'une des sous-divisions du bassin du Brahmapoutre présentent une
tendance décroissante alors que celles d'une autre sous-division présentent une
tendance croissante. Il en est de même de deux des trois sous-divisions du bassin du
Meghna. La série des précipitations du bassin du Gange ne montre aucune persistance
Markovienne que l'on peut au contraire mettre en évidence sur deux sous-divisions
communes aux bassins du Brahmapoutre et du Meghna.
INTRODUCTION
The Ganges and Brahmaputra rivers originate on the southern and northern slopes of
the Himalayas, respectively. They traverse thousands of kilometres to debouch into
the Bay of Bengal, after meeting 200 km upstream in central Bangladesh. By
Open for discussion until / June 1999
846
M. O. Mirza et ai
comparison, the Meghna River is smaller. It originates in the southern slopes of the
mountain range to the north of Manipur, India. These three river basins cover about
1.75 x 106 km2 across five different countries—China, Nepal, India, Bhutan and
Bangladesh. They are unique in the world in terms of diversified climate. For
example, the Ganges basin is characterized by low precipitation in the northwest of
its upper region and high precipitation in the areas along the coast. The high
precipitation zone and dry rain shadow areas are located in the Brahmaputra basin,
whereas the world's highest precipitation area is situated in the Meghna basin.
These rivers support more than half a billion people in their vast basin areas. They
supply water for food and fibre production and industrial and domestic purposes.
Knowledge of the changes in precipitation (in terms of trends and persistence) is crucial
for the irrigated agriculture and other water resource planning in the basin-sharing
countries. It is especially important for the downstream countries to have a clear understanding of the characteristics of precipitation in the upstream areas as the basis for water
sharing agreements pertaining to the common rivers. For example, in 1997, Bangladesh
(downstream user) and India (upstream user) plunged into dispute over the occurrence of
very low flow (less than 1417 mJ s'1) in the Ganges River at Farakka over a significant
period of the dry season (January-May). India claimed that this was due to low winter
and summer rainfall in northern India (Mirza, 1997), while Bangladesh argued that
winter and summer rainfall played virtually no role in the dry season flow of the Ganges
River and that the low flow was the result of water diversions upstream of Farakka.
Analysis of variations in precipitation are thus required to clarify the extent to which
such low flow events are due to natural climatic variability or to human abstraction.
Some studies on the trends and persistence in precipitation have been carried out
for the whole of India (Parthasarathy & Dhar, 1975; Shukla, 1987; Sarker &
Thapliyal, 1988; Parthasarathy & Mooley, 1978). However, none of these studies
examined the combined Ganges-Brahmaputra-Meghna (GBM) basins, nor have any
studies been conducted for Nepal in the upstream Ganges basin nor downstream in
Bangladesh where the three river basins meet. The aim of this study is therefore to
determine the trends and persistence in precipitation in various parts of the Ganges,
Brahmaputra and Meghna river basins in order to give an entire GBM basin-wide
perspective on precipitation changes.
THE STUDY AREAS
The study areas are the three individual river basins: the Ganges, Brahmaputra and
Meghna. The Ganges basin is comprised of 12 meteorological subdivisions in India,
all of Nepal and the Ganges basin Bangladesh. The Indian meteorological subdivisions are: Sub-Himalayan West Bengal, Gangetic West Bengal, Bihar Plateau,
Bihar Plains, East Uttar Pradesh, West Uttar Pradesh, Haryana, East Rajasthan,
West Madhaya Pradesh and East Madhaya Pradesh. Part of the Ganges basin in
China was excluded because of the lack of data. The Brahmaputra basin partly covers
North Assam, South Assam and Sub-Himalayan meteorological subdivisions in India
and the Brahmaputra basin in Bangladesh. Bhutan was excluded as the precipitation
Trends and persistence in precipitation in the Ganges, Brahmaputra and Meghna river basins
847
Fig. 1 The study area in the Ganges, Brahmaputra and Meghna basins.
data were unavailable. The Meghna basin is comprised of parts of the North Assam
and South Assam meteorological subdivisions in India and the Meghna basin in
Bangladesh. The study area and basin subdivisions are shown in Fig. 1.
DATA
Annual precipitation data for the three river basins were collected from various
recognized sources. For the Ganges, Brahmaputra and Meghna basins in India, data
848
M. O. Mirza et al.
were collected from the Center for Ocean-Land-Atmosphere Research (COLA),
Maryland, USA. The COLA received the original data set from the Indian Institute
of Tropical Meteorology (IITM), Pune, India. Quality and details of the data until
1984 are given in Parthasarathy et al. (1987). However, information on later years is
not available (Paolino, 1995, personal communication). Nepalese data were derived
from the published records of the Department of Meteorology, His Majesty's
Government of Nepal. The quality of the original data, especially with regard to
measurement errors, is not fully known. This is particularly important for the snowy
region where measurement errors could be higher than for other regions. Data for
the Bangladesh parts of the three river basins were derived from the records of the
Department of Meteorology and Bangladesh Water Development Board (BWDB).
Meteorological subdivisions in the Ganges basin in India have 124 years
(1871-1994) of precipitation records, while in Bangladesh, the record is 31 years.
The Nepalese stations have a maximum of 20 years of record. The subdivisions in
the Brahmaputra and Meghna basins in India have a total of 81 years of precipitation
records, while in Bangladesh, the records are 31 years and 29 years, respectively.
The COLA data set does not contain any missing observations. The Nepalese
data were derived from averaging precipitation from 66 stations. Some 36 stations
have 1-10% missing observations. Stations in the Bangladesh part of the basins have
2% missing observations.
In lieu of missing observations, values were estimated from nearby correlated
stations. First, correlations among all stations were determined and stations having
correlation coefficients equal to or greater than 0.5 were identified. Then, station-tostation distances were calculated using coordinates. The missing observations for a
particular month for a station were then calculated using the ratio of the mean precipitation of the station with a missing record to the adjacent stations multiplied by
the precipitation of that month. A maximum of five stations were used. The advantage of this method is that it captures the precipitation pattern of the surrounding area
of a station with missing observations. The annual precipitation was determined by
summing up the monthly values. After filling in the missing observations, the means
and standard deviations were computed for the complete time series and compared
with those of the incomplete time series. The differences in the means and standard
deviations were found to be statistically insignificant.
METHODS
This paper examines trends and persistence in the annual precipitation series of the
three river basins. Trends are examined by applying the following statistical tests and
regression analysis.
The Mann-Kendall rank statistic, x (Kendall & Stuart, 1961)
This non-parametric test has been extensively applied for trend detection in a number
of geophysical variables, such as rainfall over Banjul, Gambia (Anyadike, 1993) and
Trends and persistence in precipitation in the Ganges, Brahmaputra and Meghna river basins 849
India (Parathasarathy & Dhar, 1975); air temperature in Greece (Giles & Flocas,
1984); and in convection and rainfall in Northern Amazonia (Chu et al., 1994). The
statistic x is computed from:
4/7,
x=
'
-1
(1)
y }
N(N-l)
where nl is the number of values larger than the fth value in the series subsequent to
its position in the series of TV values.
The expected value of x in a random series is zero, and its variance is given by:
1
9N(N~\)
{
'
The ratio of x to its standard deviation 8T (i.e. x/ôT) is an indication of trend in the
data. When there is an absence of a trend in the data series, this ratio lies within the
limits of ±1.96 at the 95% level of confidence.
Student's Mest (Salas et al, 1980)
The classical /-statistic (modified for taking into account the effect of persistence) is
used for testing whether the difference in two means x, and x2 for the period 1 and 2
is significant, i.e.:
, = JtiZ^
(3)
n, • n-,
with
zo,--*i) 2 +ZO/-*2) 2
n, + «, - 2
- \
(4)
The null hypothesis is rejected if \t\ > tx_ajl, nx + n2 - 2.
However, in order to consider the effect of "persistence" in the trend analysis,
Mitchell et al. (1966) suggested the following modifications for determining t value.
Values of r, are calculated independently for the two periods of record to which
x, and x, refer. The values of r, for these two periods may be denoted as (/,), and
(r,) 2 , respectively. Then TV,' and N2', the corrected estimates for the periods «, and n2,
are determined applying the following two equations.
^
'
T
^
N.=„7.—±LL.
1 +
('l)2
(5)
(6)
M Q. Mirza et al.
850
The values of Nt' and N2' are substituted for nx and n2 in equations (3) and (4). The
value of t is selected for (TV/ + N2' - 2) degrees of freedom at a given level of
significance.
Regression analysis
For the trend detection, regression analysis was also conducted with time as the
independent variable. Slope of the regression line indicates a per year increase or
decrease in precipitation. Significance of the slope is tested by determining the t
value with the following equation and is distributed with n - 2 degrees of freedom:
t
=—,
!—=
(7)
" JMSK/SZ
where, MSE is residual mean square and Sxx is:
{£*,
SIt=Xv-^~
,=i
(8)
n
The null hypothesis (H0: slope bx is not significantly different from zero) is rejected if
r<)|
>
Kiii.n-i
•
However, in the presence of a statistically significant r,, the least square
procedure tends to produce too small values of the standard error of bx. Consequently, this produces a larger t value than would otherwise be the case. Many
procedures are available for removing the effect of r, for trend detection by
regression analysis (Chow, 1964; Bowerman & O'Connell, 1990; Hirsch el al.,
1982; Wigley & Jones, 1981). Wigley & Jones (1981) suggested increasing the
variance by the following factor in order to take into account the effect of
autocorrelation:
\+r
2r(l-rN)
f\N,r) = —;
rr
(9)
J
l-r
N{l-r)~
where r is the lag-1 autocorrelation, and TV is the number of observations. In this study,
the method suggested by Wigley & Jones (1981) was applied for its simplicity.
Persistence is the tendency for successive values of a climatological series to
"remember" their antecedent values, and to be influenced by them (Giles & Flocas,
1984). Thus, large values of an element such as precipitation tend to be followed by
large values and vice versa, so that runs of values of similar magnitudes tend to
persist throughout the sequence. The best known measure of this tendency is the
lag-1 autocorrelation, which is given by the equation:
I(X,-X)(X, +I -J0
(=i
I(A^X)
2
(10)
Trends and persistence in precipitation in the Ganges, Brahmaputra and Meghna river basins 85 I
where the X, is the annual precipitation at time t, N is the length of the record, and
X is the mean annual
value appropriate for
The significance
Gaussian distribution
-1 ±
precipitation. The null hypothesis is that r, is no larger than the
randomness.
of r, is tested using the one-tail 95% confidence point of the
(Mitchell et al., 1966). The test value (r,), is computed from:
IMSjN^l
( ' . ) , = — ^
(H)
A negative value of r, gives indication of marked high frequency (i.e. short-period)
oscillations in the precipitation series. On the other hand, positive values indicate
Markov linear type persistence. Gilman et al. (1963) have suggested that this
persistence has the property r„ = (r,)". Accordingly, the lag-2(r2) and lag-3(r3)
autocorrelations have been computed and compared with (r,)2 and (r,) 3 , respectively.
If the relationships r2 = (r,) 2 and r3 s (r,) 3 are satisfied, then Markov persistence can
be assumed. This means, that a large annual precipitation total for one year, for
example, would be followed by an equally large total for the next year.
RESULTS
Trends
Following the methods described above, Kendall's x, T/8 T and regression slopes have
been calculated for all the 16 subdivisions covering the GBM basins. The results are
presented in Table 1.
The Ganges basin For the Ganges basin, values of the Kendall's x and the slope
of the regression equations vary from subdivision to subdivision. Out of the 10
meteorological subdivisions in India, only one case (East Madhaya Pradesh) x/ST is
found to be significant at the 95% confidence level. Regarding the slope of the
regression equation for this same subdivision, the null hypothesis is rejected at the
5% significance level, which suggests a decreasing trend in precipitation in this subdivision (Fig. 2). Precipitation in the Bangladesh part of the basin shows an
increasing trend (Fig. 3) as demonstrated by the Kendall's x, x/5T and the slope of the
regression equation. Both have been found significant at the 95% confidence level.
The Brahmaputra basin Each of the North Assam and South Assam subdivisions has 81 years (1901-1981) of precipitation record. The Brahmaputra subdivision of Bangladesh has 31 years of record.
The values of Kendall's x, x/ôT and slopes of the linear regression lines are not
significant for North Assam. However, for South Assam, the means of precipitation
for the periods 1901-1940 and 1941-1981 were found to be statistically different, as
indicated by Student's r-test. Taking into account the effect of autocorrelation, the
negative slope of the regression line was also found to be significant for South
852
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Trends and persistence in precipitation in the Ganges, Brahmaputra and Meghna river basins
853
2000
1871
1881 1891
1901 1911 1921 1931 1941 1951 1961 1971 1981 1991
Year
Fig. 2 Annual precipitation (mm) in East Madhaya Pradesh meteorological
subdivision. The regression line shows a decreasing trend.
2200
1985
1990
1995
Fig. 3 Annual precipitation (mm) in the Bangladesh part of the Ganges basin (19631993).
Assam. The decreasing trend is especially evident from about 1960, as can be seen in
Fig. 4. In contrast, from 1960 onwards the precipitation in the Brahmaputra basin in
Bangladesh shows an increasing trend, significant at 95% confidence level for the
Kendall's x, x/S- and slopes of the linear regression line (Fig. 5).
The Meghna basin As stated before, the Indian part of the Meghna basin is
within North Assam and South Assam subdivisions. Precipitation in South Assam
indicates a decreasing trend, as noted above. For the Meghna basin in Bangladesh,
Kendall's i, x/8T have been calculated as 0.14 and 1.08, respectively. They have not
854
M. Q. Mirza et al.
Fig. 4 Annual precipitation (mm) in South Assam meteorological subdivision. The
regression line shows a sharp decreasing trend.
995
Fig. 5 Annual precipitation (mm) in the Bangladesh part of the Brahmaputra basin
(1963-1993).
been found significant at the 95% confidence level. However, slopes of the linear
regression line (S = 20.41, t = 2.13, p = 0.04, d/ = 1, 29) have been found
significant (Table 1). Therefore, conservatively it can be concluded that precipitation
in Meghna subdivision in Bangladesh is increasing (Fig. 6).
Persistence
The Ganges basin In order to determine persistence in the annual precipitation
series of the individual meteorological subdivisions in India, Nepal and Bangladesh
Trends and persistence in precipitation in the Ganges, Brahmaputra and Meghna river basins 855
2800
1960
1965
1970
1975
1980
1985
1990
1995
Year
Fig. 6 Annual precipitation (mm) in the Bangladesh part of the Meghna basin.
parts of the basin, lag-l(r,), lag-2(r2) and lag-3(r3) autocorrelations were calculated
and the results presented in Table 2. It is seen from Table 2 that out of
12 meteorological subdivisions, six subdivisions show negative autocorrelation and
the remaining six subdivisions show positive autocorrelation. A negative value of r, is
indicative of marked high frequency (i.e. short-period) oscillations in the preTable 2 Autocorrelation for the Bangladesh, Nepal and the meteorological subdivisions of the Ganges
basin in India.
River basin and
meteorological subdivision
Autocorrelation
lag-1
Ganges basin:
0.004
Sub-Himalayan West Bengal*
Gangetic West Bengal
-0.078
Bihar Plateau
0.028
0.013
Bihar Plain
East Uttar Pradesh
0.080
West Uttar Pradesh
-0.040
-0.030
Haryana
-0.012
East Rajasthan
West Madhaya Pradesh
0.049
East Madhaya Pradesh
-0.001
Nepal
0.155
Ganges basin in Bangladesh
-0.120
Brahmaputra basin:
North Assam**
0.01
South Assam**
0.43 (0.000 06)
Brahmaputra basin in
-0.03
Bangladesh
Meghna basin:
Meghna basin in Bangladesh
0.138
Note: probability level is shown within the parentheses
* part includes the Brahmaputra basin;
** parts include the Meghna basin.
lag-2
-0.060
-0.013
0.040
-0.100
-0.047
0.030
0.047
0.100
0.160
0.090
0.089
-0.150
0.16
0.41 (0.00)
-0.05
0.134
for South Assam;
lag-3
-0.0003
0.076
0.071
0.019
-0.150
0.072
0.120
0.064
0.070
0.170
-0.110
0.300
0.27 (0.03)
0.39 (0.00)
0.32
0.21
856
M. O. Mina et al.
cipitation series. On the other hand, positive values indicate Markov linear type
persistence.
None of the positive r, values is significant at the 95% confidence level, though
the values of r2 and r3 are greater than (r,)2 and (r,)3. This is an indication that while
Markov linear type persistence exists in the series, it is not statistically significant.
The values of negative r, were also found statistically insignificant. The precipitation
series may thus be considered to be random.
The Brahmaputra basin Lag-1, lag-2 and lag-3 autocorrelations for the areaweighted precipitation series as well as for the individual subdivisions have been
calculated. Results are presented in Table 2. The results show that lag-K^)
autocorrelation values for all the subdivisions are positive. This indicates Markov
linear type persistence in the precipitation series. Lag-l(r,) autocorrelation for South
Assam is highly significant at the 95% confidence level and confirms the Markov
linear type persistence. Lag-l(r,) autocorrelation for North Assam is not significant.
However, a further check has been made by computing lag-2(r2) and lag-3(r3) and
comparing these with (r,)2 and (r,)3, respectively. For North Assam and South
Assam, r2 and r3 have been found greater than (r,)2 and (r,)3 and r3 is significant at the
95% confidence level. This indicates presence of Markov linear type persistence in
the precipitation series of these two subdivisions. Precipitation in the Bangladesh part
of the basin is random.
The Meghna basin As noted above, Markov linear type persistence is present in
North Assam and South Assam subdivisions, which the Meghna basin shares with the
Brahmaputra basin. In the Meghna basin subdivision in Bangladesh, lag-l(r,) was
calculated to be +0.14 and is not significant at the 95% confidence level. Values of
r2 and r3 were greater than (r,)2 and (r,)3 but not significant. Therefore, it can be
concluded that Markov linear type persistence is not present in the precipitation
series in the Bangladesh part of the basin. The results indicate that the annual
precipitation regime in northeastern India is different from that of northeastern
Bangladesh.
DISCUSSION AND CONCLUSIONS
The comparison of results with regard to persistence and trends in precipitation in the
three river basins is rather difficult due to unequal lengths of record. Measurement
and processing errors incorporated in the time-series data might have some
implications for the results. Generally, information on data quality are not available
and not well documented in South Asia (Mirza & Dixit, 1997). Nonetheless, for
analyses of long-term trends and persistence of aggregated (annual) data, it is
unlikely that common measurement errors would affect the results in a substantive
manner.
The Ganges, Brahmaputra and Meghna river basins represent diversified climatic
regions. Analyses indicate that among the three river basins, precipitation in all sub-
Trends and persistence in precipitation in the Ganges, Brahmaputra and Meghna river basins
857
divisions of the Ganges is stable; only the East Madhaya Pradesh and the Ganges
basin subdivision in Bangladesh are exceptions which show decreasing and increasing
trends, respectively. A decreasing trend in precipitation in only one subdivision (8%
of the total basin) should not affect substantially the mean annual runoff in the
Ganges basin. However, it may have implications for rain-fed agriculture in that
particular subdivision. Increasing precipitation may be beneficial for the rain-fed
agriculture in the Bangladesh part of the basin but limited to a certain threshold.
Overall, the stable precipitation is favourable for water resources planning in the
basin.
Until 1960, annual precipitation in South Assam subdivision looks stable, but
significant change has occurred in the period 1961-1981 (Fig. 4). Decreasing
precipitation in only South Assam subdivision (about 9% of the basin) might not have
affected the runoff of the Brahmaputra river. However, it may have adverse effects
on the rain-fed agriculture and availability of water for the population living in the
mountain area of the South Assam subdivision. This underscores the need for
detailed analysis of monthly and seasonal precipitation of this subdivision which
would probably reveal specific changes in precipitation patterns. Increased
precipitation in the Bangladesh part of the Meghna basin may cause longer
inundation in the Meghna depression which is flooded every year to varying extent.
If the water is not drained out in time, cultivation of boro rice (a type of rice planted
in January-February and harvested in April-May) crop may suffer.
The presence of a Markov linear type persistence in a precipitation series means
that a large (or small) annual precipitation total for one year is more likely to be
followed by a large (or small) total for the next year. Thus the precipitation from
year to year is not random. The presence of Markov linear type persistence in the
precipitation series of the Brahmaputra and Meghna basins in Assam in India
suggests that precipitation in these two areas is not a random phenomenon from year
to year, and that the chance of occurrence of high (or low) precipitation in consecutive years is higher than would otherwise be the case. Knowledge about this nonrandom distribution is particularly useful, for example, in assessing the risk of crop
inundation or drought in the North and South Assam meteorological subdivisions.
The presence of Markov linear type persistence therefore helps in the formulation of
policies that may be used to avert crop failures or to plan for food security in the face
of "back-to-back" years of feast or famine.
The causes of the changes in precipitation revealed by this analysis are unknown.
It is unlikely that these changes can be attributed to global climate change. In the first
instance, physical causes related to changing patterns of monsoon precipitation ought
to be investigated.
Overall, the analyses indicate that annual precipitation in the Ganges basin is
stable (excluding exceptions for two subdivisions). However, precipitation in the
Brahmaputra and Meghna basins display rather contrasting pictures in the
upstream and downstream areas. These changes in precipitation now need to be
investigated in a detailed, comprehensive manner, in order to discern the specific
implications for the hydrological system and economic activities of the region for
the future.
858
M. Q. Mirza et ai
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Received 12 September 1997; accepted 5 February 1998