a study in Damodar River of West Bengal, India

Arab J Geosci DOI 10.1007/s12517-015-2046-6

ORIGINAL PAPER

Dam-induced changes in flood hydrology and flood frequency of tropical river: a study in Damodar River of West Bengal, India Sandipan Ghosh 1,2 & Sanat Kumar Guchhait 3

Received: 4 March 2015 / Accepted: 10 September 2015 # Saudi Society for Geosciences 2016

Abstract The Damodar River of West Bengal is popularized as ‘Sorrow of Bengal’ due to massive unpredictable destruction in the monsoonal floods, recorded since 1665. After establishment of Damodar Valley Corporation (DVC) of India in 1948, Tilaiya, Tenughat, Konar, Maithon and Panchet dams (Jharkhand) and Durgapur barrage (West Bengal) are built to regulate flood flow to a certain limit. But, as the floods were unpredictable in pre-dam phase, even now, lower Damodar Basin is not secure from the monsoonal floods. To assess the flood risk and nature of flood discharge, we have focused here to fit extreme value distribution (EVD) to the annual peak flow of the Damodar River using mainly Gumbel and log Pearson type III distributions. Pre-dam (1934–1957) and post-dam (1958–2007) flood frequency analysis has significantly projected maximum probable flood discharge of Damodar at Rhondia with a certain return period of occurrence, and it provides an idea about future flood risk in lower Damodar Basin.

Keywords Flood . Flood risk management . Flood climate . Gumbel distribution . Log Pearson type III distribution . DVC

* Sandipan Ghosh [email protected] Sanat Kumar Guchhait [email protected] 1

Department of Geography, Chandrapur College, Chandrapur, Barddhaman, West Bengal 713145, India

2

Baburbag, Paschim Para, P.O. Rajbati, Barddhaman, West Bengal 713104, India

3

Department of Geography, The University of Burdwan, Barddhaman, West Bengal 713104, India

Introduction Any flow which is relatively high and which overtops the natural or artificial banks in any reach of a river may be called a ‘flood’ (Reddy 2011). River floods can occur directly when the amount of rainfall is of sufficient quantity that the land surface cannot absorb and then redistribute excess water fast enough to prevent a surface accumulation of water (i.e. inundation), or floods can occur indirectly such as when a river overtops its banks during peak flow (Whitfield 2012). The term ‘flood climate’ is probably introduced by Hayden (1988) who has developed a global classification of floodproducing climates based on the mean seasonal state of the atmosphere. Hirschboeck (1988) introduces the discipline of ‘flood hydroclimatology’ which has detail focus of hydrometerologic-scale atmosphere activity, while, at the same time, seeking to set that activity within a broader spatio-temporal, climatic perspective of flood. Traditional approaches to analyzing floods assumed a guise of determinism though concepts such as design flood dealt with uncertainty implicitly. Now, a risk-based approach recognizes that unpredictability is fundamental to decisions about how to deal with flooding. In present decade, flood risk management (FRM) involves the process of real-time data gathering; risk assessment; appraisal of options; and making, implementing and reviewing decisions to reduce, control, accept or redistribute risks of flooding (Hall 2014). One of main and fundamental aspects of FRM is the reliance upon rational analysis of flood risk which can lead to reduce flood-forecasting problems and develop complete understanding of dynamic flood hydrology and flood frequency. A lot of money is invested for flood mitigation and protection using both structural and non-structural measures in every year. But, the flood forecasts or prediction can only provide very short period of forecast in an accurate form, which may

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not allow us to accept estimated magnitude and return period of next flood events (Mujere 2011). India is one of the monsoon-dominated countries that have been seriously affected by the floods on multiple occasions, and about 32 million people are affected by the floods in each year (Banerji 1950; Kale 2006). It has been found that 3.8 million-hectare area of West Bengal is considered as flood prone by the Central Water Commission (CWC) of India in 2000 and the Damodar River (an important tributary of Bhagirathi-Hooghly River System) is a major contributor of floods in the southern districts of West Bengal (Central Water Commission 2000; Rudra 2002; Kale 2003). Hydrometeorological floods of the Damodar River Basin (DRB) were precisely analyzed by Satakopan (1949), Banerji (1950), Bhattacharya (1959), Rao (1951), Sen (1985), Sengupta (2001), Rudra (2002, 2009) and Bhattacharyya (2011). It is found from the literatures that a high discharge at Rhondia (exceeding 200,000 ft3 s−1 or 5660 m3 s−1) on any date is much correlated with the rainfall recorded on the date and the preceding 2 days. The effect of dams on Damodar River network is analyzed by Bhattacharya (2000), Majumder et al. (2010) and Ghosh and Mistri (2013, 2015). The most impressive works are done by Sanyal et al. (2013, 2014a, b) and Chatterjee et al. (2014a, b) who successfully employ the hydrodynamic models (e.g. LISFLOOD-FP and HEC-HMS) to route very high-magnitude downstream floods in the Damodar River using digital elevation and discharge data. To check the peak discharge of monsoon period since 1940s, the Damodar Valley Corporation (DVC) of India had been set up the large dams in the upper catchment. It is found that dam construction induces a hydrogeomorphic instability phenomenon into the fluvial system and the river is forced to enter in a new equilibrium (Assani et al. 2006). Fluvial systems are the most sensitive elements of the landscape. For this reason, any shift in environmental conditions, including large-scale anthropogenic activities, instigates a rapid response from the fluvial systems (Kale et al. 2004; Singhvi and Kale 2009). So, the pre-dam and post-dam condition of river discharge is completely different, but analyzing the trend of both conditions, we can establish an empirical equation to predict the flood discharge of a given return period. Having great fertility and agricultural potentiality of Damodar floodplain, this region (known as ‘Rice Bowl of India’) is a desirable location for the human and his agro-based activities, but it is observed that post-flood damages occasionally exceed an acceptable limit. Therefore, a precise estimation of maximum flood discharge and threshold level of peak flow (including return period of occurrence) should be calculated in a rational and scientific way. Though discharge is a random process, but we can assume that annual maximum (or peak) discharge is an extreme hydrological event of a fluvial system (Chow et al. 1988; Raghunath 2011). As the important studies done by Benson (1968), Hann (1977), Oberg and Mades (1987), Vogel and McMartin (1991), Perr and Morris (1994), Griffs

et al. (2007), Ewemoje and Ewemooje (2011) and Sathe et al. (2012), the log Pearson type III distribution (LP3) has been selected as the base uniform method in comparison to other methods of flood frequency analysis. Alila and Mtiraoui (2002), Kidson and Richards (2005), Millington et al. (2011) and Zakaullah et al. (2012) have compared the widely used methods of flood frequency analysis (extreme value distribution (EVD), Gumbel, log normal, log Pearson type III, etc.) in selected river basins of the world to judge the applicability and accuracy. To study flood frequency of the Damodar River, it is important to fit the annual peak (or maximum) flow data (considering as maximum flood discharge in a year) in a probability distribution which can give us the satisfactory results regarding flood prediction for a given return period. Impact of dams on the annual peak flows significantly influences the flood frequency distribution through changing the natural hydrological regimes (Assani et al. 2006). Unpredictably, the dams and barrages of DVC now control the annual flow of lower Damodar River, and simultaneously, the flow regulation of monsoon period is currently responsible for downstream floods in the southern districts of West Bengal. To the best of the author’s knowledge and literature survey, no previous studies have been attempted so far to model annual peak discharge of the Damodar River using the Gumbel and LP3s. So, this flood frequency analysis of pre-dam and post-dam phases tries to study the complexity and trend in the annual peak discharge of lower Damodar River and to make significant statement on the potential flood discharges of a certain return periods. To reach that goal, we have set forth following three prime objectives 1. Analyzing the importance of flood climate in DRB 2. Securitizing the temporal trend of river discharges in relation to resultant effects 3. Assessing the dam-induced changes in the flood frequency and future trend

Materials and methods Study area The Damodar River rises in the Khamarpat Hill (Palamau District, Jharkhand) of Chotanagpur Plateau at about 609.57 m above mean sea level (Chandra 2003; Bhattacharyya 2011). Flowing easterly direction along the Gondwana coal-rich faulted trough, Damodar meets with the Barakar River near Dishergrah, and finally in a sudden southerly direction below Barddhaman and Hooghly districts, it bifurcates into (1) the Kanki-Mundeswari and (2) the Amta Channel-Damodar and joins with Bhagirathi-Hooghly River near Falta about 48.3 km downstream of Kolkata (Chandra

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2003; Bhattacharyya 2011). After crossing the Gondwana Formation (Permian to Early Cretaceous) of Asansol– Raniganj–Durgapur areas, the river enters into laterite Rarh Plain of Lalgarh Formation (Early to Late Pleistocene) and finally crosses the Quaternary litho-units of Sijua Formation (Late Pleistocene to Early Holocene), Chuchura Formation (Early to Late Holocene) and Hooghly Formation (Late Holocene to Recent) (Ghosh and Guchhait 2014a). For sample study, we have selected the Quaternary segment of middle to lower DRB in between Rhondia (Galsi I Block) and Paikpara (Jamalpur Block). The latitudinal extension of selected area ranges from 22° 00′ to 23° 22′ N, and longitudinal extension varies from 87° 28′ to 88° 01′ E. Its funnel-shaped basin area (Fig. 1a, b) is about 23,370 km2, spreading in the states of Jharkhand (73.7 %) and West Bengal (26.3 %) (Majumder et al. 2010). Since 1933, the discharge of the Damodar River is measured at ‘Anderson Weir’ near Rhondia (only discharge measuring gauge station on lower Damodar River situated in West Bengal under the control of Irrigation and Waterways Dept., Govt. of West Bengal), and at Rhondia, the estimated upper catchment area of Damodar is 19,920 km2. The lower fan-deltaic basin (less than 50-m elevation) comprises the densely populated blocks of eastern Barddhaman, Hooghly and Howrah districts where the monsoon floods are frequent mostly along the riparian tracts and distributaries of the Damodar River. Principally to mitigate downstream floods and to tamp monsoonal peak flow, the authority of Damodar Valley Corporation (DVC) has been constructed the dams and barrages, viz. Tilaiya on the Barakar River (1953), Konar on Konar River (1955), Durgapur Barrage on the Damodar River (1955), Maithon on the Barakar River (1957), Panchet (1959) and Tenughat (1978) on the Damodar River (Chandra 2003; Ghosh and Guchhait 2014b). Methodology Hydrologic processes evolve in space and time in a manner that it is partly predictable, or deterministic, and partly random. Such a process is called a ‘stochastic process’ (Chow et al. 1988; Rao and Hamed 2000). The prime objective of statistical techniques is to extract the essential information from a set of hydrologic data, reducing a large set of numbers to a small set of components (Chow et al. 1988). Flooding is one of the most pervasive natural hazards to impact negatively up on the activities of human beings and requires various responses including construction, forecasting and land use management (Kidson and Richards 2005). To some degree, all of these that require hazard or risk assessment are identified in the form of a flood frequency analysis (FFA) (Kidson and Richards 2005). The long continuous and reliable hydrological records (74-year peak flow records of the Damodar River at Rhondia) are an indispensable part in understanding of monsoon floods and in the flood risk assessment (Kale

2006). Statisticians agree that floods of small frequency are random variables, and they argue that even the highest design floods are strictly random variables and should be treated as elements of statistics of extreme values (Al-Mashidani et al. 1978). To employ statistics, we have been collected secondary data and spatial information mostly from Damodar Planning Atlas (1967), book entitled ‘Lower Damodar River, India: understanding the human role in changing fluvial environment’ (Bhattacharyya 2011). official website of Irrigation and Waterways Department of West Bengal, topographical sheets (73 M/7, M/11, M/12, M/15, M/16, N/13 and 79 A/4) of Survey of India (SOI, 1970–1974, Representative Fraction (RF) 1:50,000) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) image (USGS 2013). The records of peak flow of lower Damodar River at Rhondia (from 1934 to 2007) are collected from the aforesaid book (Appendix C, D, E and F). As, currently, DVC dams control the peak flow, then entire FFA is subdivided into two phases: (a) pre-dam period (1934–1957) and (b) post-dam period (1958–2007). We have also employed inflow and outflow discharge data of Panchet–Maithon (Bhattacharyya 2011) and Durgapur Barrage (IWD 2014) to depict the flow regulation and reservoir operation in flood period. To relate rainfall with peak discharge, the meteorological data (CWC 1994) of selective locations (situated at upper catchment of Damodar) is used here. For the spatio-temporal change analysis of thalweg, active river bed, mature bars and islands, we have used NF 45-2 Series U502 toposheet (1922 – 43, R.F. 1:250,000) of Corps of Engineers US Army and satellite images of Landsat MSS (1970) and IRS P6 LISS III (2013). After collecting and storing secondary data, we have employed statistical techniques, viz., mean, standard deviation, skewness, curvilinear regression, probability distribution, confidence limit and chi-squared test, etc. for hydrological interpretation of stream flow data in Microsoft Excel 2003 and SPSS 14.0 software. Quantitative techniques It is hypothesized that pre-dam and post-dam annual peak discharge of the Damodar River at Rhondia fits Gumbel probability distribution (GPD) and LP3 significantly and there is no distinction between observed and expected extreme values. Encounter probability is needed if a flood of a long recurrence interval is chosen; there is always a possibility that the flood can be exceeded more than once during the interval (Raghunath 2011). The magnitude of an extreme event is inversely related to its frequency of occurrence, very severe events occurring less frequently than more moderate events. We have applied here GPD, LP3, Chow method and stochastic method. Emil Julius Gumbel (1891–1966) has developed the model of distribution of the maximum (or the minimum) of a number of samples of various distributions (Gumbel 1941; Al-

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Mashidari et al. 1978; Chow et al. 1988; Rao and Hamed 2000; Raghunath 2011; Reddy 2011). As per this distribution, the exceedance probability (P) is given by

Fig. 1 a Spatial extent of the Damodar River Basin in the states of Jharkhand and West Bengal and b close view of study area, including sample locations of field survey along the Damodar River

P ¼ 1−e−e−y ¼ 1=T r

by comparing it with the standard normal variate for that significance level. The reduction in degrees of freedom (df) is calculated as p=s=1, where s is the number of parameters used in fitting the distribution. Degree of freedom will be (n −p), where n is the number of categories or cells in table.

ð1Þ

If XT denotes the magnitude of the flood with return period of Tr years [Tr =1/(1–e−e−y) ], X T ¼ X mean þ K T :σ

ð2Þ

where KT is the ‘frequency factor’ (yT −ymean /σn), yT is the reduced variate, ymean is the mean of reduced variate and σn is the standard deviation of reduced variates (calculating these from table value of Gumbel’s distribution). Though, without referring to the table, Chow and Powell have modified the calculation of frequency factor (Al-Mashidani et al. 1978). Pearson type III distribution is a skew distribution with limited range in the left direction, usually bell shaped (Raghunath 2011). LP3 has the advantage of providing a skew adjustment, and if the skew is zero, the log Pearson distribution is identical to the log normal distribution (Chow et al. 1988; Rao and Hamed 2000; Griffs et al. 2007; Raghunath 2011). The United State Water Resource Council (1967). Hann (1977) and Oberg and Mades (1987) adopt this distribution to achieve standardization of procedures. The values of x for various recurrence intervals are computed from logx ¼ logxmean þ K T σlogx

ð3Þ

where KT is the frequency factor, tabulated in respect of skew coefficient and recurrence intervals (Hann 1977). To include the annual peak discharge data of the Damodar River into following analysis, we should first judge the homogeneity and stationary of the data. In this test, two samples of size p and q with p1800 m3 s−1) of three flood years are sharply high from the observation of pre-dam hydrographs. The late monsoonal peak values suggest that the regulation of stream flow is not controlled totally by those constructions. Fig. 7 a Pre-dam and post-dam variation in annual flood hydrographs, b pre-dam condition of annual average discharges in flood years of 1943, 1950 and 1953 (one annual maxima in August) and c post-dam annual average discharges in flood years of 1959, 1970 and 1978 (two annual maxima in September and October)

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Dam-induced quantitative variability in flood magnitude Since 1958, through the examination of actual combined inflow–outflow discharge data of Panchet and Maithon dams, we have observed that 80 to 32 % of flood moderation (declining trend) has been achieved during important flood episodes up to 2007 (Fig. 8a). In spite of flood moderation by DVC dams ,the flood occurred severely in 1959, 1978, 1999,

Fig. 8 a Combined peak flow regulation by Panchet and Maithon dams in selective flood years to represent the range of peak inflow–outflow into the Damodar River from 1958 to 2007 (data source: Bhattacharyya 2011)

2000, 2006, 2009 and 2013, demonstrating the current vulnerability of lower valley to sudden floods. Voorduin’s (one of architects of Damodar Valley Planning) design flood discharge of 28,321 m3 s−1 (resulting from a rainstorm of 50.8 cm in upper catchment) and controlled capacity of 7080 m3 s−1 at Rhondia are not fulfilled by DVC due to less completion of total project. Presently, DVC reservoirs have flood reserve of only 1863 million m 3 whereas it was

and b operation of Durgapur barrage to regulate inflow–outflow in the Lower Damodar River at the time of tropical cyclone Phyline (2013)

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projected to 3596 million m3. Some of the examples of postdam flood situation are presented here to depict the operation of DVC reservoirs and Durgapur barrage. During the flood of 1959 (1–2 October), the peak inflow into the reservoirs of Maithon and Panchet was 17,641 m3 s−1 of water which was moderated to 8155 m3 s−1. Then, the outflow from Durgapur barrage was 9911 m3 s−1 due to contribution from intermediate catchment. The September flood of 1978 (26–27 September) was an all-time high with a combined inflow peak of 21,900 m3 s−1 (Table 4). If this peak was allowed to pass without any flow moderation, it would have generated a probable peak of 33,414 m3 s−1 at Durgapur barrage (Chandra 2003). Under the fluence of tropical depression (4–8 September 2009), heavy to very heavy rainfall was experienced since 14:00 h on 4 September 2009 at few places of in Orissa and entire Lower Gangetic Plain of West Bengal during next 60 h. The huge rainfall, which was 92.7-mm rain on 7t September (275 mm of rainfall in 5 days: 4–8 September 2009), is the highest since May 25, 2009, when Kolkata received 93.1 mm at the time of Super Cyclone Aila. The release of 250,000 m3 s−1 of water from Maithon, Tenughat and Panchet and sudden release of 5094 m3 s−1 water from Durgapur barrage on 6 September 2009 led to severe flooding of some areas in the districts of Hooghly, Howrah, Barddhaman and East Medinipur. Over 2,000,000 people are directly affected in 5221 villages, including damages of 30, 443 ha of crop land. Again, unprecedented rainfall during Phyline (13–15 October 2013) in the upper catchment areas of Damodar and consequent release of flood water from the different reservoirs under DVC system resulted in significant downstream discharge from Durgapur barrage. The maximum release of 4620 m3 s−1 was recorded on 15 October 2013 from Durgapur barrage due to which the river gauge at Champadanga and Amta crossed effective danger level (EDL) on the next day (IWD 2014). This was resulted by the combined 9736 m 3 s −1 outflow from Maithon and Panchet reservoirs during 14 to 15 October 2013. The recorded gauge level at Champadanga on 16 October was 13.93 m against EDL 13.50 m, and at Amta, this value was 6.56 m against EDL 6.24 m. The peak outflow from Durgapur barrage is almost similar to inflow (i.e. less storage or flood reserve) in between 28 September to 4 October 2013 (Fig. 8b),

Table 4 Performance of DVC reservoirs (Maithon and Panchet) in September 1978 flood (m3 s−1)

releasing more than 4500 m3 s−1 peak discharge into lower Damodar. There is a marked difference of annual peak flow in between pre-dam (1933–1956) and post-dam period (1958– 2007). It is found that mean Qmax (i.e. maximum peak discharge of period) of pre-dam phase is 8378 m3 s−1 with coefficient of variation (CV) of 0.45, and with installation of dams and canal system, the mean Q max is reduced to only 3522 m3 s−1 with CV of 0.63. A peak flow of above 18, 000 m3 s−1 has been recorded three times in August 1913, 1935 and October 1941 (Saha 1979; Bhattacharyya 2011). In post-dam period, the highest combined inflow at Maithon and Panchet dams was recorded as 21,070 m 3 s −1 on September 27, 1978. At present, extremely high-magnitude floods are disappeared, but the frequency of low-magnitude floods is still remained high in lower Damodar Basin (Fig. 9). According to E. L. Glass report (1924), the high to moderate flood discharge (5664 to 12,744 m3 s−1) was observed frequently at Raniganj gauge station (almost 80 km upstream from Rhondia) in between 1857 and 1917. Up to 1956 at Rhondia weir, Damodar River had been experienced extremely high discharge (greater than 12,744 m3 s−1) episodes, but after establishment of DVC flood regulation system, the river has experienced low-magnitude floods (less than 5664 m3 s−1). In old records, the Damodar River has always been referred to as a river of sorrow. W. W. W. Hunter in 1876 writes that, during floods, the rainwater used to pour off the hills through hundreds of channels with such suddenness that water heaped up to form dangerous head waves, locally known as ‘harkaban’(i.e. flash flood) (Lahiri-Dutt 2006; Bhattacharyya 2011; Ghosh 2013). The absolute flood discharge of a river is not as important with regard to geomorphic change as the ratio between peak discharge and mean annual discharge (i.e. FFMI) (Ghosh and Guchhait 2014b). Log deviation from mean discharge to extreme peak value is exponentially (Yc =0.1525× 2.04) related to FFMI (applying Eq. 14). It means that the episodes of high degree of deviation between Xm and X are associated with high FFMI and extreme floods in the Damodar River, having coefficient of determination of 0.96 (Fig. 10a). This index nearer to 1.0 or above indicates the high degree of flash flood episode with some

With DVC dams

At Maithon and Panchet At Durgapur

Without DVC dams

3 hourly peak inflow

3 hourly peak outflow

3 hourly peak inflow

3 hourly peak outflow

21,917

4617

26,958

26,958

10,732

10,732

33,414

33,414

Source: Chandra (2003) and Bhattacharyya (2011)

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Fig. 9 Three-phase variation of different magnitudes of floods in the Damodar River at Raniganj and Rhondia to understand the trend of occurrence (1857 to 2007)—extremely high-magnitude floods (above 12,744 m3 s−1), high-magnitude floods (8496–12,744 m3 s−1), moderate magnitude floods (5664–8496 m3 s−1) and low-magnitude floods (below 5664 m3 s−1) (data source: Bhattacharyya 2011)

geomorphic change within the basin (Kochel 1988). As the series is divided into pre- and post-dam periods, the value of M from pre-dam period is M=3.923 and for the post-dam period is M=3.567. FFMI is gained maximum value in between 1950 and 1957 (pre-dam phase) and consecutively in between 1958 and 1969 (post-dam phase). Then, 33 years (1970–2003) of record show that FFMI was significantly low than the previous, that is why in these years, no extreme floods (except 1978) had been occurred. But, the last one (2004–2007) is approaching towards FFMI of 1 which signifies forthcoming flood episodes following the years of 2006 (7035 m3 s−1) and 2007 (8853 m3 s−1). The fluctuation of FFMI (1934 to 2007) is associated with variability of south-west monsoon and strong tropical depressions in lower Gangetic plains (Fig. 10b). The high FFMIs of 1950–1957 and 1958–1969 are associated with 118 and 217 numbers of cyclones of Bay of Bengal, respectively, but low FFMI of 1988–1995 is related with only 95 numbers of cyclones and good flood regulation by DVC. It is very important to note that floods of peak flow of 8496 m3 s−1 or more had been occurred 37 times between 1823 and 2007, influenced by the severe tropical cyclones of Bay of Bengal, like ‘Aila’ of 2009 and ‘Phyline’ of 2013. FPI (applying Eq. 15) is an effective measure to judge the height of peak flow above the maximum confidence limit of flood occurrence. In pre-dam period, 62.5 % of annual peak flows (10,675–6075 m3 s−1) and FPI are situated in between the FPI range of 4.272–2.433, having confidence limit at 99 % significance level. In post-dam period, 34.88 % of annual peak flow (3800–2020 m3 s−1) and FPI of 0.710–0.354 are situated in 99 % significance level of confidence limit. Basically, FPI greater than 1 signifies flood years which are observed in 1959, 1971, 1978, 2006 and 2007 (Fig. 11). The standard deviation of FPI is much greater (1.501) in pre-dam phase, but due to flow regulation, the deviation is now much less (0.383). Additionally Cf (i.e. coefficient of flood) is estimated

at 6.52 (very high flood height from base flow) and 1.12 (very low flood height from base flow), respectively, in pre- and post-dam condition. With increasing distance from the Anderson Weir, Rhondia, the channel dimensions of Ab, Wb and W/D are now gradually decreased with low competence of accommodating peak discharge. The estimated maximum and minimum bankfull discharges are 5848 m3 s−1 near Belut and 529 m3 s−1 near Jamalpur, respectively, with the Ab of 6360 and 812 m2 at those sections. The W/D is significantly reduced at downstream from 206.6 to 12.1, reflecting the narrowness of sinuous channel (Fig. 9a). The Qmax (applying Eq. 16) is projected approximately 10,213 and 12, 393 m3 s−1 in between Ramgoplapur and Gohagram. This is decreased up to 2106–3048 m3 s−1 in between Jamalpur and Paikpara (Fig. 12b) Based on above analysis, it is understood that the lower Damodar River has lost carrying capacity to accommodate excess water within its active limit because due to siltation of river bed whenever the dams release water into the channel, the bankfull stream flow occasionally overtops the both banks and inundates the adjoining floodplain of Barddhaman, Hooghly and Howrah districts. If the annual maximum discharge crosses the limit of 2000 m3 s−1 (estimated at Rhondia), the flood will definitely occur in the lower part of basin. It is a common situation in the period of late monsoon rainfall and cyclonic rainfall. Recently, due to severe tropical cyclone of Bay of Bengal, Phyline (October 2013), the catchment of Damodar receives 320–350-mm rain within 3 days and sudden release of excess water (almost 8950 m3 s−1) from the reservoirs of Maithon and Panchet inundates the 16 blocks of Hooghly and Howrah districts (The Hindu 2013). FFA using Gumbel and LP3s Using Gumbel and LP3 distributions, we have found that in pre-dam period (1934–1957), the peak discharge of 18, 112 m3 s−1 (1935) has attained a return period of 50 years with 2 % of probability of occurrence (Table 2 and Fig. 3). But, the peak discharges of 12,002 m3 s−1 (1938); 11,012 m3 s−1 (1951); and 10,811 m3 s−1 (1942) have attained only 6.7-year (15 %), 4.9-year (20.4 %) and 4.6-year (22 %) return periods, respectively. This signifies the quick occurrence of high magnitude of flood in the lower valley in between 1934 and 1955. It is estimated that any discharge above 7080 m3 s−1 (standard project flood) at Rhondia creates flood flow of moderate–high magnitude. So, on this basis, we have found the ferocity and high frequency of flood discharge in uncontrolled Damodar River in up to 1957. Surprisingly, the return period of 7075– 9561 m3 s−1 discharge is only 1.7–3.2 years (59 to 31 % of probability). In this unsymmetrical distribution, the general slope of the fitted curve is given by coefficient of variation (CV=σ/Xmean) which is 0.45 for pre-dam period (nearly 45°

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Fig. 10 a Deviation from mean discharge to extreme peak value is exponentially related to FFMI; i.e. high degree of log deviation is ultimately transformed into high magnitude of flash floods in lower Damodar River (after Ghosh and Guchhait 2014b) and comparison with world average FFMI (after Kale 2003). b Temporal pattern and expected

trend (i.e. expected curve with coefficient of determination, R2 of 0.605) of FFMI showing dominance of flash floods in three episodes, viz., 1950– 1957, 1958–1969 and 2004–2007 and successive three calm periods up to 2003

of steep slope). It indicates the short return period of high magnitude of annual maximum discharge. The departure from the straight line is given by the coefficient of skew i C S ¼ Σ ðX ‐ X mean Þ3 =ðn‐1Þσ3 ð20Þ

coefficient of floods (Cf) indicates the general magnitude of the floods in a particular river (A = 19,920 km2 at Rhondia gauge station); hence, it fixes the height of the curve above the base. It is estimated as 6.52 for pre-dam period. From this distribution, we have found that the mean discharge of that period is 8378 m3 s−1 (greater than 7080 m3 s−1) with standard deviation of 2235 m3 s−1 (Table 5 and Fig. 13).

It is 1.24 (positively skewed distribution), and it indicates a more or less same range in the magnitude of floods. The

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Fig. 11 Post-dam (1958–2007) temporal variation of FPI with the peaks of highest flood flow and estimated FPI confidence limits of occurrence at 99 % significance level

Implementation of Damodar River Valley Project has radically altered the peak discharge value (Table 6 and Fig. 14) through controlled regulation of water from last two terminal big dams (Panchet on the Damodar River and Maithon on the Barakar River) and Durgapur Barrage. From the calculation, we have found mean discharge of 3522 m3 s−1 (less than 7079 m3 s−1) with standard deviation of 2235 m3 s−1. For

Fig. 12 With increasing downstream distance from Rhondia, a the width-depth ratio and b annual maximum discharge are significantly reduced in the lower Damodar River

50 years of record (1958–2007), CV is 0.63 (much higher than previous). It indicates large range in the magnitude of floods than pre-dam period. CS is more or less same, but Cf is reduced to 1.12 only. It indicates the lower magnitude of floods. Based on 50 years of data, peak flood discharge of 10, 919 m3 s−1 (1978) has attained a return period of 124 years with only 0.81 % of probability of occurrence, but it was only

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we have calculated χ2 for pre-dam and post-dam periods. The null hypothesis is that there is no difference between the observed and theoretical value and Gumbel’s method and LP3 fits the data significantly. The results of χ2 testing suggest that the null hypothesis is accepted in both pre-dam and post-dam periods with up to 99.99 % of confidence level. Because in Gumbel distribution, the calculated χ2 (pre-dam—11.2012 and post-dam—2.8488) is greater than the theoretical χ2 (0.05 significance level–30.14 and 0.01 significance level–36.19 in pre-dam period and 0.05 significance level– 61.66 and 0.01 significance level–69.66 in post-dam period). Again, in LP3, the calculated χ 2 (pre-dam— 16.9017 and post-dam—7.9521) is greater than the theoretical χ2. So, there is very limited difference between observed and theoretical peak discharge values in both methods. But, in terms of universal applicability, the LP3 is the best method to forecast flood discharge in this region. It can be said that the future prediction of

4–5 years (22 % of probability) in pre-dam period. It signifies the performance of DVC in flood regulation. The analysis tells that flood discharge of 7035–8883 m3 s−1 has attained return period of 14–39 years, having 7– 2.5 % of probability (Fig. 10). The return period of 2–2.7 years (50–37 % of probability) is associated with peak discharge of 2811–3855 m3 s−1. At last, it is found that, presently, the annual peak discharge of Damodar follows the equations Gumbel Distrbution−QT ¼ 3522 þ 2235 K

ð21Þ

log Pearson Type III Distribution−QT ¼ 3:451 þ 0:3176 K T

ð22Þ

We have successfully fit the extreme values to GPD and LP3, and it is required to test whether this distribution is significant or not to project future floods. Getting the theoretical or expected peak discharge of the consecutive years (1934–2007) from the methods, Table 5

Flood frequency analysis of the Damodar River at Rhondia (1934–1957) Gumbel distribution

Log Pearson type III

Rank

Year of peak flow

Peak flow (m3 s−1)a

Xmean

Return period (years)

Exceedance probability (%)



Remarks

1 2 3 4 5 6 7 8 9 10 11

1935 1941 1938 1951 1942 1950 1946 1940 1956 1943 1953

18,112 17,942 12,002 11,012 10,811 9561 9133 8773 8579 8384 8287

9734 9564 3624 2634 2433 1183 755 395 201 6 −91

50 47 6.7 4.9 4.6 3.2 2.9 2.6 2.5 2.3 2.3

2 2.13 14.9 20.4 21.7 31.3 34.5 38.5 40 43.5 44.4

25.00 12.50 8.33 6.25 5.00 4.17 3.57 3.13 2.78 2.50 2.27

4 8 12 16 20 24 28 32 36 40 44

n=24 Mean SD CV CS Cf

12 13 14 15 16 17 18 19 20 21 22 23 24

1947 1939 1949 1954 1936 1948 1944 1937 1957 1952 1934 1945 1955

8235 7989 7696 7407 7075 6500 5905 5876 5658 5120 4793 4514 1714

−143 −389 −682 −971 −1303 −1878 −2473 −2502 −2720 −3258 −3585 −3864 −6664

2.2 2.1 2 1.9 1.7 1.5 1.4 1.4 1.3 1.2 1.2 1.1 1

45.5 47.6 50 54.1 58.8 66.7 71.4 74.1 76.9 83.3 87 90.9 100

2.08 1.92 1.79 1.67 1.56 1.47 1.39 1.32 1.25 1.19 1.14 1.09 1.04

48 52 56 60 64 68 72 76 80 84 88 92 96

SD standard deviation, CV coefficient of variation, CS coefficient of Skew, Cf coefficient of flood a

Source: Bhattacharyya (2011)

8378 3752 0.44784 1.24 6.52

Arab J Geosci Fig. 13 Fitting Gumbel distribution to pre-dam trend of annual peak discharge and estimated return period with empirical logarithmic equations of flood prediction

peak flood discharge of different return period can be possible or may provide good results for flood forecasting in lower Damodar River. Projecting flood discharge of variable return period using different methods of FFA As the discharge of a river is very uncertain and random phenomenon in respect of the monsoonal rainfall, runoff and the carrying capacity of reservoirs, it is very difficult to predict the exact peak discharge of a certain return period for flood forecasting and management. We have compared the annual flood series results of Gumbel distribution and LP3, but now, we have paid focus on the predictable flood discharges of variable return periods, viz., 2, 5, 10, 25, 50, 100 and 200 years, using Gumbel’s method, LP3, Chow’s method and stochastic method. The resultant equations are 1. Gumbel Distrbution—QT ¼ 3522 þ 2235 K

ð23Þ

2. log Pearson Type III Distribution—QT ¼ 3:451 þ 0:3176 K T 3. V: T: Chow method—QT ¼ a þ b X T

ð24Þ ð25Þ

where QT =Annual flood peak of T return period X T ðfrequency factorÞ ¼ logðlog T =log T −1Þ

ð26Þ

a and b=parameters estimated by the method of moments from the observed data Pre‐dam equation−QT ¼ 3942:21−7490:61 X T

ð27Þ

Post‐dam equation−QT ¼ 3141:17−4345:08 X T

ð28Þ

4. Stochastic method—One of the well-known stochastic equations based on annual flood data using Poisson probability law and theory of sums of random number of random variables is . QT ¼ Qmin þ 2:3ðQmean −Qmin Þ log n f ⋅n T ð29Þ where nf

Qmin Qmean

Number of recorded floods, counting only one for the same flood peak occurring in different years Minimum peak discharge in a series Mean peak discharge

Pre‐dam equation—QT ¼ 1714 þ 15327:4 logT

ð30Þ

Post‐dam equation−QT ¼ 413 þ 7150:7 logT

ð31Þ

Except the results of stochastic method, the results of other three methods provide a very close estimation in predicting flood discharge. It is noticed that the predictable discharges of Gumbel and Chow methods are very close to each other. In pre-dam period (Table 7), four estimated discharges of 2-year return period are 7815 m3 s−1 (Gumbel), 8110 m3 s−1 (LP3), 7845 m3 s−1 (Chow) and 6328 m3 s−1 (stochastic) which are high above the critical limit (7080 m3 s−1 at Rhondia, mentioned by DVC). The annual flood series of pre-dam period

Arab J Geosci Table 6

Flood frequency analysis of the Damodar River at Rhondia (1958–2007) Gumbel Distribution


Rank Year of peak flow


Xmean– Return period (years)




Remarks

1

1978

10,919

7397

124

0.81

51.00

1.96

n

50

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2007 1959 2006 1995 2000 1973 1999 1976 1958 1987 1971 1984 1961 1998 1977 1967 1975 1993

8883 8792 7035 6522 6387 5726 5690 5297 4682 4567 4556 4512 4371 4249 4156 4138 3855 3816

5361 5270 3513 3000 2865 2204 2168 1775 1160 1045 1034 990 849 727 634 616 333 294

39 37 14 11 10 7 6.5 5.5 4 3.8 3.7 3.7 3.4 3.2 3.1 3.1 2.7 2.7

2.56 2.7 7.14 9.09 10 14.3 15.4 18.2 25 26.7 27 27.4 29.4 31.3 32.3 32.8 37 37.7

25.50 17.00 12.75 10.20 8.50 7.29 6.38 5.67 5.10 4.64 4.25 3.92 3.64 3.40 3.19 3.00 2.83 2.68

3.92 5.88 7.84 9.80 11.76 13.72 15.68 17.64 19.60 21.56 23.53 25.50 27.45 29.41 31.37 33.34 35.30 37.25

mean SD CV CS Cf

3522 2235 0.63454 1.21134 1.163

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

1970 1996 1963 1986 1968 1960 1985 1994 1990 1965 2003 1997 1974 1991 1983 2004 1964 1989

3782 3627 3542 3455 3391 3389 3317 3298 3146 2811 2496 2407 2392 2184 2098 2058 1977 1933

260 105 20 −67 −131 −133 −205 −224 −376 −711 −1026 −1115 −1130 −1338 −1424 −1464 −1545 −1589

2.6 2.4 2.4 2.3 2.2 2.2 2.2 2.1 2 1.8 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3

38.5 41.7 42.6 44.4 45.5 45.9 46.5 47.6 50 57.1 62.5 65.4 66.2 70.4 71.9 73 74.6 75.2

2.55 2.43 2.32 2.22 2.13 2.04 1.96 1.89 1.82 1.76 1.70 1.65 1.59 1.55 1.50 1.46 1.42 1.38

39.21 41.17 43.13 45.10 47.06 49.02 50.10 52.94 54.90 56.86 58.82 60.78 62.74 64.70 66.67 68.63 70.59 72.55

38 39 40 41 42 43 44 45 46

1962 2001 2002 1969 1981 1988 1992 1972 2005

1926 1859 1859 1740 1635 1632 1443 1434 1140

−1596 −1663 −1663 −1782 −1887 −1890 −2079 −2088 −2382

1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1

75.8 76.3 76.9 78.7 81.3 82 84 84.7 88.5

1.34 1.31 1.28 1.24 1.21 1.19 1.16 1.13 1.11

74.51 76.47 78.43 80.39 82.35 84.31 86.27 88.23 90.19

Arab J Geosci Table 6 (continued) Gumbel Distribution


Rank Year of peak flow


Xmean– Return period (years)




47 48 49 50

666 502 421 413

−2856 −3020 −3101 −3109

94.3 95.7 96.6 97.1

1.09 1.06 1.04 1.02

92.15 94.11 96.08 98.04

1982 1966 1980 1979

1.1 1 1 1

Remarks

SD standard deviation, CV coefficient of variation, CS coefficient of skew, Cf coefficient of flood a

Source: Bhattacharyya (2011)

predicts that 100-year floods will be above 21,000 m3 s−1 and only 5 years flood will be greater than 10,000 m3 s−1. The massive floods of 1935 (18,112 m 3 s −1 ), 1938 (17, 942 m3 s−1), 1941 (12,002 m3 s−1), 1942 (10,811 m3 s−1) and 1951 (11,012 m3 s−1) signify the high frequency of abnormally large floods in lower Damodar River. But, now, the river is controlled by large dams, so, the situation is completely different than the pre-dam period. The predictable discharge of 2-year return period will be above 2500 m3 s−1 but less than 3200 m3 s−1. If the annual flood series follows the trend of post-dam period, the 5-year flood will be above 5300 m3 s−1 and 100-year flood will be above 11,000 m3 s−1. The only year of 1978 witnessed the peak discharge of 10,919 m3 s−1. But, the lower Damodar Basin is not completely safe from annual floods. The flood is inevitable due to the declining carrying capacity of reservoirs and over-siltation of river reaches (Bhattacharyya 2000). According to FAO (2015). the Damodar River annually yields sediment of 1400 tkm−2 year−1 with annual average runoff of 500 mm and it carries sediment load of 28,000,000 t year−1. That transported bulk of sediments get deposited in the river and reservoir beds. Estimates suggest a 274 and 381 % increase in annual rate of silt deposition in the Maithon and Fig. 14 Fitting Gumbel distribution to post-dam trend of annual peak discharge and estimated return period with empirical logarithmic equations of flood prediction

Panchet reservoirs, respectively, declining their actual life span of 59 and 78 years, respectively (Petr and Morris, 1994). Due to rapid land use conversion at upper catchment (e.g. deforestation, mining, expansion of fallow land and soil erosion), the sediment yield rate increases from 1109 to 2387 m3 km2 year−1 with an increase in siltation rate of Panchet reservoir from 0.033 (1990) to 0.047 cm per year (Majumder et al. 2012). The aggradation and siltation of active river bed can be inferred from the progressive accretion of mature mid-channel bars, point bars and islands. The spatiotemporal analysis of two segments of Damodar reflects (Fig. 15) an increasing reduction of active river bed from pre-dam period (1922–1943) to post-dam period (2013) and escalating accretion of bars (i.e. growth of mature bars in area on the active river bed of Damodar). It signifies the siltation of active bed and gradual loss of cross-sectional area and carrying capacity of lower Damodar River. According to Chandra (2003). there are reaches below Amta where the Damodar is not even capable of carrying a discharge of 1415 m3 s−1. So, it is necessary to estimate the return periods of present bankfull discharges of the different downstream reaches of lower Damodar River. To estimate the bankfull discharge (m3 s−1), we have calculated the bankfull volume of three

Arab J Geosci Table 7 Comparison of projecting flood discharges (m3 s−1) with variable return periods

KT

QT


XT

Pre-dam

Gumbel

2 5 10 25 50 100 200 Post-dam

−0.521 −1.014 −1.334 −1.751 −2.057 −2.360 −2.662 Gumbel

−0.15 0.894 1.572 2.456 3.105 3.747 4.387

7815 11,732 14,276 17,592 20,028 22,437 24,838

2 5 10 25 50 100 200

−0.521 −1.014 −1.334 −1.751 −2.057 −2.360 −2.662

−0.157 0.821 1.455 2.283 2.891 3.491 4.091

3170 5357 6776 8625 9982 11,326 12,665

selected channel segments of the Damodar River, viz., (1) Rhondia to Jujuti segment, (2) Jujuti to Chanchai segment and (3) Chanchai to Paikpara segment. Importantly, we have found three bankfull discharges of aforesaid segments which are 4011, 2366 and 1542 m3 s−1, respectively. Considering the DVC-mentioned critical discharge limit of 7080 m3 s−1, it is very essential to find out the probable return periods of the four bankfull discharges (flood discharges) using the postdam annual flood series and aforesaid methods (Table 8). From the table, it has been found that the return period of 7079 m3 s−1 discharge ranges from 8.55 to 14 years at Rhondia. Similarly, the other return periods of three discharges range from 1.18 to 3.18 years. So, it is cleared that the threshold level of peak discharge (with short time span) is very small in respect of the post-dam annual flood series and carrying capacity of the Damodar River. For that reason, whenever the last two terminal dams (Panchet and Maithon) released excess water, the riparian tracts of Barddhaman, Hooghly and Howrah districts (covering lower Damodar Basin) had been experienced monsoonal floods in 1958, 1961, 1976, 1978, 1995, 1999, 1987, 2000, 2006 and 2007, having very low magnitude of peak discharge in comparison to pre-dam period.

Conclusion The decision to live in a Damodar floodplain, for a variety of perceived benefits, is one that is fraught with difficulties. So, to save from difficulties and risk, we should adopt FFA for

KT

QT

Log Pearson type III 0.136 8110 0.855 11,429 1.161 13,216 1.435 15,066 1.588 16,181 1.710 17,140 1.809 17,989 Log Pearson type III 0.136 3119 0.855 5273 1.161 6592 1.435 8054 1.588 9016 1.710 9863 1.809 10,593

XT

QT

V.T. Chow method −0.521 7845 −1.014 11,538 −1.334 13,935 −1.751 17,058 −2.057 19,350 −2.360 21,620 −2.662 23,882 V.T. Chow method −0.521 3177 −1.014 5320 −1.334 6710 −1.751 8522 −2.057 9851 −2.360 11,168 −2.662 12,480

QT

Stochastic method 6328 12,427 17,041 23,140 27,754 32,368 36,982 Stochastic method 2566 5411 7564 10,409 12,562 14,714 16,867

management purpose. The above hydrologic analysis has brought into focus some important information on the predam and post-dam variability of stream flow in the furious lower Damodar River of West Bengal. The flood climate of DRB has much potentiality to generate heaviest rainfall and resultant flood flow with annual influence of deep tropical depressions and cyclones in post-dam decade. The rainfall– discharge graph with exponential model suggests that 24-h heaviest rainfall of more than 200 mm (at upper catchment) is able to generate downstream flood flow of more than 6000 m3 s−1 at Rhondia. There is a clear difference between pre- and post-dam flood frequency and peak discharge (in each statistical model fitted), emphasizing the dam-induced flood moderation. The Damodar River has undergone morphological adjustment following the construction of the dams, and this will also impact on the extent and frequency of inundation. It is identified that in pre-dam period, the flood peaks and intensities are too high, but the duration was small. The installation of DVC dams has moderated the high peaks but increased the duration of floods in a year. The furious monsoon discharge of 6081–10,676 m3 s−1 (pre-dam confidence limit at 99 % significance level) is reduced up to 2574– 4470 m3 s−1 due to reservoir storage and diversion of flow through canals. DVC dams truly reduce the peak of flood flow from the base flow, as coefficient of flood (CS) is decreased significantly from 6.52 (pre-dam period) to 1.12 (post-dam period) At present, the floods have more chance to occur in between September and October due to shift of hydrograph peak from August to September. Particularly, in lower Damodar River, the low-magnitude floods (less than

Arab J Geosci

Fig. 15 Spatio-temporal changes (1922–1943 to 2013) in active area of river bed, thalweg and areal span of mature mid-channel bars, point bars and islands of Damodar River at a Somsar and b Belkash to reflect the river bed aggradation and siltation

5664 m3 s−1) are more common in recent decades in place of extremely high-magnitude floods (greater than 12, 744 m3 s−1). Importantly, FFMI of this river is still well above of great Indian rivers and it is annually influenced by onset of south-west monsoon, timing of cyclones and performance of DVC flood regulation system. Whenever the deviation of maximum discharge from minimum discharge is aggravated,

Table 8 Predicted return periods of probable bankfull discharges in lower Damodar River Potential

Estimated return period in years

Bankfull discharge (m3 s−1)

Gumbel

LP3

Chow

Stochastic

7080 4011 2366 1542

14.0 2.90 1.45 1.21

13.2 2.92 1.56 1.18

14.2 2.91 1.48 1.23

8.55 3.18 1.87 1.44

the lower part of basin is affected by recurrent floods, giving less cope-up time to inhabitants. Based on chi-squared test and coefficient of determination, LP3 distributions are found to be best suitable for predicting the possible annual peak discharges of the Damodar River. Flood frequency of less than 5000 m3 s−1 of discharge is well forecast by this distribution, as records suggest. The carrying capacity to accommodate bankfull discharge is reduced downstream up to 1542 m 3 s −1 , and the recurrence interval of maximum 4011 m3 s−1 or less is estimated as 2–3 years only. For that reason, whenever DVC dams release excess water in the late monsoon period, the low-lying riparian areas of lower Damodar Basin (covering Barddhaman, Hooghly and Howrah districts of West Bengal) are annually inundated by low-magnitude flood for a couple of days, destructing crops and habitats. Principally, unpredicted monsoon rainfall (as the basin located in major rainstorm zones of eastern India), high runoff yield of upper funnel-shaped catchment, SE to NW path cyclones (oriented along the basin, from mouth to

Arab J Geosci

source), bottle neck location of this basin in the Bengal Delta, siltation of river and reservoirs, rigorous modification of active river bed through structures, delinking of distributaries, malfunction of DVC canals and, most importantly, man’s affinity to live close to the Damodar River have aggravated cumulatively the risk of flood in this particular flood potential region. The ultimate outcome of this study is that we cannot predict the amount of rainfall and runoff accurately at all locations as well as resultant flood flow in India, but here, the quantitative analysis of flood hydrology and FFA of annual extreme values have provided a statistically significant tool to project potential flood discharge of a given return period in a dam-controlled alluvial river of West Bengal. Acknowledgments We are very much thankful to Prof. Sutapa Mukhopadhyay (Dept. of Geography, Visva-Bharati), Prof. Shukla Acharjee (Dept. of Applied Geology, Dibrugarh University), Prof. Ashis Sarkar (Dept. of Geography, Chandannagar Govt. College) and Prof. Priyank Pravin Patel (Dept. of Geography, Presidency University) for their critical review and suggestions about this research work. We are thankful to Prof. Joy Sanyal (Dept. of Geography, Presidency University) for providing his great research papers on the flood modelling of the Damodar River. We are sincerely grateful to Prof. Abdullah M. AlAmri (Editor-in-Chief, Arabian Journal of Geosciences) for giving his support and suggestions to enrich the manuscript.

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