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-to-station 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)

N(N-l) y }

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

(4) n, + «, - 2

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 ^ (5)

N.=„7.—±LL. (6) 1 + ( ' l )2

850 M Q. Mirza et al.

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:

{£*, S I t = X v - ^ ~ (8)

, = i 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 precipitation. The null hypothesis is that r, is no larger than the value appropriate for randomness.

The significance of r, is tested using the one-tail 95% confidence point of the Gaussian distribution (Mitchell et al., 1966). The test value (r,), is computed from:

- 1 ± 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/8T 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

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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 (1963-1993).

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 pre-

Table 2 Autocorrelation for the Bangladesh, Nepal and the meteorological subdivisions of the Ganges basin in India.

River basin and meteorological subdivision

Ganges basin: Sub-Himalayan West Bengal* Gangetic West Bengal Bihar Plateau Bihar Plain East Uttar Pradesh West Uttar Pradesh Haryana East Rajasthan West Madhaya Pradesh East Madhaya Pradesh Nepal Ganges basin in Bangladesh Brahmaputra basin: North Assam** South Assam** Brahmaputra basin in Bangladesh Meghna basin: Meghna basin in Bangladesh

Autocorrelation

lag-1

0.004 -0.078 0.028 0.013 0.080

-0.040 -0.030 -0.012 0.049

-0.001 0.155

-0.120

0.01 0.43 (0.000 06)

-0.03

0.138

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

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

Note: probability level is shown within the parentheses for South Assam; * part includes the Brahmaputra basin; ** parts include the Meghna basin.

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 area-weighted 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 non-random 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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