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Changes in the rainfall pattern are a challenge for filling schedule of reservoir, when it is fulfilling various demands. In monsoon fed reservoirs, the target remains for attaining full reservoir capacity in order to meet various demands during non-monsoon period and the flood control. The planners always eye towards the inflow trend and perspective frequency of rainfall in order to counter the extreme events. In this study, the case of Hirakud reservoir of Mahanadi basin of India is considered as this reservoir meets various demands as well as controls devastating floods. The inflow trend has been detected by using Mann Kendall test. The frequency analysis of monthly rainfall is calculated using L-moment program for finalizing a regional distribution. The falling trend in inflow to reservoir is visualized in the month of July and August. The Wakeby distribution is found suitable for the monthly rainfall of July, September and October, where as in June and August, General Extreme Value (GEV), General Normal (GN) and Pearson Type-III (PT-III) distributions are found suitable. The regional growth factors for the 20, 40, 50 and 100-year return period rain-falls along with inflow to reservoir observed between 1958-2010 are calculated in this study as a referral for reservoir operation policy.

Hirakud reservoir as a multipurpose dam resolving many demands of state of Odisha. The operation of the reservoir is governed by a specified rule curve and it is supposed to attain its full reservoir level at the end of October 31st (end of monsoon season) in order to meet the demands till start of the monsoon season (end of May). In this regard the rainfall and its distribution of upstream districts play pivotal role in filling schedule of the reservoir. There are numbers of studies in these regards and a few of them are discussed. Reference [

L-moment approach has been applied to many events in number of cases for finding parent distribution. In case of flood frequency analysis L-moment has been applied in many occasions. However, in different rainfall events application of L-moment is seen in cases like [

The Hirakud reservoir of Mahanadi basin cover almost 83,400 sq km of catchment area out of total catchment of 141,589 sq km and covering most part of two states like Chhatisgarh and Odisha (

The reservoir Hirakud was commissioned since 1958 as a multipurpose project. A catchment of 83,400 sq km drains into reservoir Hirakud covering 24 districts of four states fully or partly (

searching a trend in rainfall and inflow as it may has been put direct impact on the operation and management of reservoir for fulfilling the necessary demands. As the study is related to inflow of reservoir, districts of its upstream part are only considered.

1) Trend Detection: To identify trend in climatic variables with reference to climate change, the Mann-Kendall test has been employed by a number of researches with temperature, precipitation and stream flow data series ( [

The Mann-Kendall trend test is based on the correlation between the ranks of a time series and their time order. For the statistics S is calculated as Equation (1). This statistic represents the number of positive differences minus the number of negative differences for all the differences considered as

S = ∑ i = 1 n − 1 ∑ j = i + 1 n sgn ( x j − x i ) (1)

where, n is the number of total data points, x i and x j are the data values in time series i and ( j > i ) , respectively, and sgn ( x j − x i ) is the sign function as:

sgn ( x j − x i ) = { + 1 , if ( x j − x i ) > 0 0 , if ( x j − x i ) = 0 − 1 , if ( x j − x i ) < 0 (2)

The variance of Mann- Kendall test is calculated by Equation (3) as

V a r ( S ) = n ( n − 1 ) ( 2 n + 5 ) − ∑ i = 1 m t i ( t i − 1 ) ( 2 t i + 5 ) 18 (3)

where, n is the number of total data points, m is the number of tied groups. The tied group means a simple data having a same value. The t i indicates the number of ties of extent, i. In case of the sample size, n > 10 , the standard normal test statistic Z s is estimated by Equation (4) as

Z s = { S − 1 V a r ( S ) , if S > 0 0 , if S = 0 S + 1 V a r ( S ) , if S < 0 (4)

The positive values of Z s show increasing trends while negative values represent falling trends. As 5% significance level is taken standard for this study, the null hypothesis of no trend is rejected if | Z s | > 1.96 .

2) L-moment analysis: Three statistical measures discordancy measure, heterogeneity measure and goodness of fit measure as per L-moment approach are used in regional studies. These measures are explained by [

H i = ( V i − μ v ) / σ v (5)

For each simulated region, the measures of variability V i (where V i is any of three measures V 1 , V 2 and V 3 ) is calculated. From the simulated data, the mean μ v and standard deviation σ v of the N s i m values of V i are determined.

The critical H statistics for a region to be homogeneous is as mentioned below

H < 1 Homogeneous (6)

1 ≤ H ≤ 2 Possibly heterogeneous (7)

H > 2 Definitely heterogeneous (8)

Reference [

The measure H 2 indicates whether at-site and regional estimates will be close to each other. A large value of H 2 indicates whether or not the at-site and regional estimates will be in agreement, whereas a large value of H 3 indicates a large deviation between at-site estimates and observed data.

3) Selection of Regional Distribution: The regional distribution has been adjudged on the basis of Z-statistics as follows:

It indicates suitability of a candidate distribution to a data series and is appropriate for evaluating and comparing a distribution. The Z-statistics for the goodness of fit measure as defined by Hosking is

Z D I S T = ( Z 4 D I S T − Z 4 + B 4 ) / σ 4 (9)

D I S T = a particular distribution, Z 4 D I S T = L-kurtosis for fitted distribution, Z 4 = pooled L-kurtosis, B 4 = bias correction, σ 4 = estimate of sample variability of L-kurtosis. The Z D I S T value should be close to zero. However, a value between −1.64 and 1.64 is considered to be suitable for a fitting distribution at 10% significance level. While a number of distributions may qualify the goodness-of-fit criteria, the most potential will be one that has minimum | Z D I S T | value. The rainfall values based on different frequencies are calculated from the relationship between R t and R m , where R t is the rainfall value at particular return period t and R m is the mean rainfall.

Data Used: The district wise rainfall data from 1958-2010 is used from the India Meteorological Department (IMD) sources and the Inflow to reservoir has been obtained from Government of Odisha [

From the catchment map (

As the upstream catchment analysis is needed for finding the inflow characteristics first of all the influence area of each districts which is influencing the inflow are obtained and mentioned in

Districts | Area (sq km) | Influence area (%) |
---|---|---|

Odisha | ||

Bargarh | 800.06 | 0.96 |

Deogarh | 296.83 | 0.36 |

Jharsuguda | 2121.48 | 2.54 |

Nabarangapur | 189.44 | 0.23 |

Nuapada | 968.92 | 1.16 |

Sambalpur | 2406.83 | 2.89 |

S.Garh | 4140.66 | 4.97 |

Total | 13.10 | |

Chhatisgarh | ||

Bastar | 370.89 | 0.44 |

Bilaspur | 6742.00 | 8.09 |

Dhmatari | 4087.37 | 4.90 |

Durg | 8660.60 | 10.39 |

Janjgir-Champa | 3890.36 | 4.67 |

Jashpur | 2982.82 | 3.58 |

Kanker | 2337.85 | 2.80 |

Kwardha | 3241.60 | 3.89 |

Korba | 6520.13 | 7.82 |

Koriya | 1763.77 | 2.12 |

Mahasamund | 4774.70 | 5.73 |

Raigarh | 6963.08 | 8.35 |

Raipur | 12,517.36 | 15.01 |

Rajnandagaon | 5502.94 | 6.60 |

Surguja | 1799.44 | 2.16 |

Total | 86.54 | |

Maharastra | ||

Gadachiroli | 230 | 0.36 |

It was found that the district Raipur contains 15.01%, Durg 10.39, Raigarh 8.35, Bilaspur 8.09 and Korba 7.82% of upstream catchment. As these 5 districts, occupy 50% of geographical catchment, rainfall over these districts also to be carefully viewed as these may substantially influence the reservoir inflow.

The time series for month wise inflow to the reservoir is drawn for the period from 1958 to 2010 (Figures 3-7). The average inflows during these periods are in June 0.98, July 5.93, August 9.64, September 6.65 and in October 1.89 MAc ft. From the time series of June it is seen that, only 4 times an inflow of more than 4 MAc ft have occurred. From 1995 onwards inflow reduces to around 1 MAc ft in June. In July month during the year 1994, a maximum inflow of 22.98 and in 2001 inflow of 17.09 MAc ft was received, which resulted in flood. After 2001,

inflow near to average was being received. In August, the inflow varies continuously. An inflow of 16.384 MAc ft was received during September 2003, which again resulted in flood. The month of October remain sensitive for flood as well as filling up of reservoir. In most of the successful monsoon years, reservoir almost attains its full capacity at the end of September. So, a higher inflow may result in flood. In 2003, an inflow of 6.207 MAc ft was received in October.

The reservoir has a live storage capacity of 3.91 MAc ft and major demands like Irrigation, Power, Flood control. The average inflow and demands/releases are shown in

Applying trend analysis using Mann Kendall test, it was found that, no trends have been observed in June, September and October. In July no trend was seen at 1% and 5% significance level but a falling trend at 10%. In August, no trend was seen at 1% Significance level but falling trend at 5% and 10% (

For finding the frequency of rainfall first of one homogeneous region was established by applying L-moment approach. The unsuitable districts are removed from the homogeneous regional group as per the discordancy test. The districts having discordancy values more than 3 are discarded. The rainfall values of Bilaspur district has been discarded in all the 5 months. The suitable distributions are selected from the goodness of fit criteria. The distributions and corresponding

growth factors ( R T R m ) are shown in

culated considering all the five monsoon months for the period 1958-2010 (

Month | Average Inflow (MAc.ft) | Average Demands/Releases (MAc.ft) | ||
---|---|---|---|---|

Irrigation | Power | Spillway | ||

June | 0.98 | 0.057 | 0.53 | 0.384 |

July | 5.93 | 0.165 | 0.943 | 4.012 |

August | 9.64 | 0.172 | 1.086 | 4.928 |

September | 6.65 | 0.197 | 0.999 | 8.67 |

October | 1.89 | 0.801 | 0.801 | 3.683 |

Month | Test statistics (t) | Significance Level | ||
---|---|---|---|---|

1% | 5% | 10% | ||

June | 0.03068 | No | No | No |

July | −1.79494 | No | No | Falling |

August | −2.31655 | No | Falling | Falling |

September | −0.75173 | No | No | No |

October | 0.07671 | No | No | No |

Month | Suitable Regional Distribution | Growth factors for return periods | Remark | |||
---|---|---|---|---|---|---|

20 | 40 | 50 | 100 | |||

June | GEV | 1.767 | 1.945 | 1.998 | 2.155 | Region contains 19 districts excluding Bilaspur, Jashpur, Surguja, Koriya |

GN | 1.762 | 1.946 | 2.003 | 2.175 | ||

PT-III | 1.762 | 1.942 | 1.998 | 2.163 | ||

Wakeby | 1.78 | 1.954 | 2.004 | 2.145 | ||

July | Wakeby | 1.501 | 1.654 | 1.702 | 1.851 | Region contains 22 districts except Bilaspur |

August | GEV | 1.489 | 1.592 | 1.623 | 1.711 | Region contains 22 districts except Bilaspur |

GN | 1.486 | 1.596 | 1.63 | 1.73 | ||

PT-III | 1.486 | 1.595 | 1.628 | 1.726 | ||

Wakeby | 1.489 | 1.612 | 1.65 | 1.762 | ||

September | Wakeby | 1.671 | 1.803 | 1.84 | 1.939 | Region contains 20 districts except Bilaspur, Nawarangpur, Gadachiroli |

October | Wakeby | 2.446 | 2.721 | 2.796 | 2.994 | Region contains 22 districts except Bilaspur |

Inflow to Hirakud dam | ||||||

Inflow | GL | 2.465 | 3.184 | 3.449 | 4.406 | Taking the inflows of all monsoon months for 53 years observed between 1958-2010 |

GEV | 2.526 | 3.211 | 3.454 | 4.295 | ||

GN | 2.571 | 3.215 | 3.436 | 4.163 | ||

Wakeby | 2.586 | 3.255 | 3.483 | 4.24 |

The rainfall over five districts like Raipur, Durg, Raigarh, Bilaspur, Korba is very sensitive as this occupies almost 50% of the upstream catchment area. The rainfall during month of August is showing a falling trend. As most of the agricultural activities continue during this time a falling trend may hamper. The regional distributions like GEV, GN, PT-III and Wakeby are found suitable for month of June and August whereas Wake by found suitable for the month of July, September and October. The distributions GL, GEV, GN and Wakeby hold good for inflow forecasting taking the observed inflow series. The time series, trend analysis, regional fitting distributions and corresponding growth factors derived are useful for further planning and management of the reservoir operation.

Gupta, K.K., Kar, A.K., Jena, J. and Jena, D.R. (2017) Forecasting the Rainfall Pattern on Upstream of Hirakud Reservoir Using L-Moment for Accessing the Inflow. Journal of Water Resource and Protection, 9, 1335-1346. https://doi.org/10.4236/jwarp.2017.912085