Akshay R. Thorvat et al. / International Journal of Engineering Science and Technology (IJEST)
DESIGN FLOOD ESTIMATION FOR UPPER KRISHNA BASIN THROUGH RFFA AKSHAY R. THORVAT1 1
Assistant Professor, Department of Civil Engineering, KIT’s College of Engineering, Kolhapur, 416234, Maharashtra, India.
[email protected]
MANOJ M. MUJUMDAR2 2
Professor, Department of Civil Engineering, KIT’s College of Engineering, Kolhapur, 416234, Maharashtra, India.
[email protected] Abstract: The objective of this study is to establish a regional relationship between mean annual peak flood and the catchments area based on the frequency analysis for available annual peak flood for various gauging sites of hydro logically homogeneous region of Krishna basin, and to use the same for estimating the floods for various recurrence intervals for the catchments which are not used for analysis. This paper describes a study carried out for the Krishna basin with annual peak flood series data available for 24 sites for varying number of years. The Index flood method was used for analysis. Out of 24 sites, 4 sites were omitted after the USGS homogeneity test since they fall outside the envelope curves of homogeneity test. From the remaining 20 sites only 18 sites were considered for the analysis and data of other 2 sites were used as test sites for judging the performance of the developed regional formulae. Keywords: Design flood; Index flood method; Homogeneity test; ungauged sites. 1.
Introduction
Flood estimates are required for the design and economic appraisal of a variety of engineering works, including dam, spillways, bridges and flood protection works. Flood estimates are also required for the safe operation of flood control structures, for taking emergency measures such as maintenance of flood levees, evacuating the people to safe localities etc. Two main approaches are available for flood estimation viz., deterministic approach and statistical approach. Deterministic approach assumes that input, say, the precipitation is related to the output in a predefined manner and there is no uncertainty involved in arriving at the output, say the discharge., whereas the statistical approach treats the inter-relationship between processes as governed by theory of statistics. The inter-relationship between processes is established through the measures of correlation, the processes considered may be multivariate or, univariate. For example, the rainfall-runoff process may be considered as multivariate while, the consideration of maximum annual peak series falls under univariate process. Flood frequency analysis deals with univariate process comprising of maximum peak flow values. Before discussing the frequency analysis it is necessary to distinguish between the terminologies of prediction and forecasting from the consideration of their field use. Estimation of floods arises in hydrology from two different aspects of prognostication. The first which is usually called forecasting, involves the estimation of the values of some hydrological variable at a prescribed future instant or a forecast of the time when a particular value will occur. Forecasting the level of a flood discharge or a water level in a river some days ahead of the event is an obvious example. The second aspect, usually known as prediction is concerned not with the value of a single future event, but with the frequency of occurrence of some prescribed critical condition. For example, how often a particular level will be exceeded. Problems of first category arise most directly in the operation of hydrological controls in the broadest sense including flood warning. Problems of second category are associated with the designs rather than the operation of such controls. Design flood estimation may also be obtained through deterministic approaches say rainfallrunoff models. Therefore essentially predication deals with "how often" problem while the forecasting deals with "when" problem.
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2.
Elements of Flood Frequency Analysis
The problem of flood frequency prediction i.e. Estimation of the relationship between the magnitude of peak flow and us corresponding return period is a central one in the field of applied hydrology. Attempts to solve this problem are usually based on (a) the analysis of a record of peak flow data at the site in question and (b) use of previously established relationship between the characteristics of other catchments in the region and the parametric values of the corresponding magnitude return period relationship. The latter approach is known as regional frequency analysis used for estimating floods at sites where there is a very short peak flow record or no record available. 2.1.
Basic Assumptions in Flood Frequency Analysis
Three assumptions are fundamental to the flood frequency analysis 2.1.1.
Sample is Representative of Population:
Hydrologic data are mostly available as samples of limited sizes. Using statistical principles we extract the needed information from the available sample data and conclude about the characteristics of the population. Since any survey or any attempt cannot exhaust all possible events of a variable, we assume that the sample is representative of population. 2.1.2.
Independence of Peak Flows:
We assume that that the sample of peak flows available is independent of each other and they are assumed to be evolved from a purely random process. 2.1.3.
Homogeneity of Peak Flows:
When a series of events arranged in time show no systematic variations in time (e.g., a seasonal variation or an increasing or diminishing trend) so that we may say that the probability of an event in a period (t) is independent of the location, the series is said to be homogeneous The factors which affect the homogeneity of peak flows are the development in the catchments over time such as deforestation, urbanization, flood control works, earthquakes etc. 2.2.
Regional Flood Frequency Analysis
There have been significant developments and studies in the area of regional flood frequency analysis in India as well as abroad. Estimation of regional flood frequency parameters is performed for a specific site for two reasons: •
Because of the sample variations present in the short hydrologic records, frequency estimates of rare events based on at site frequency analysis are subjected to large error and thus unreliable. This error can be reduced by combining data from many more sites,
•
There are many more sites in the same region where hydrologic data are not available but design flood estimates are needed for the design of small structures. In such a situation regional flood frequency analysis helps in transferring the knowledge arrived from gauged sites to ungauged sites.
2.3.
Importance of Statistical Analysis in Hydrology
The random variability of such hydrologic variables as stream flow and precipitation has been recognized for centuries. The general field of hydrology was one of the first areas of science and engineering to use statistical concepts in an effort to analyze natural phenomena. The use of statistics in hydrology provides the information about various parameters and distribution of random variables of importance to design and operation of structures. These parameters and distributions are estimated as approximations from the available data because they cannot be determined exactly. Hydrologic data are mostly available as samples of limited sizes. Statistics is the main discipline enabling the extraction of needed information from data and the derivation of conclusions about the characteristics of hydrologic random variables Statistical estimates are numerical properties of samples. They are necessary in statistical modeling, or for direct use in hydrology. To be effective in application of statistics in hydrology the civil engineer or hydrologist must understand the fundamentals of statistical methods which are employed in existing hydrologic techniques.
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2.3.1. Probability Distributions Used in Hydrology: One of the major problems faced in hydrology is the estimation of design flood from fairly short data. If the length of data is more, then the same data can be used to estimate design flood, but the length of data generally available is very less. So the sample data is used to lit frequency distribution which in turn is used to extrapolate from recorded events to design events either graphically or by estimating the parameters of frequency distribution. Graphical method is having the advantage of simplicity and visual presentation. But the main disadvantage is that different engineers will fit different curves. The following continuous distributions are used to fit the annual peak discharge series. •
Normal distribution
•
Log normal distribution
•
Pearson type III distribution
•
Exponential distribution
•
Gamma distribution with two parameters
•
Log Pearson type III distribution
•
Extreme value distributions
2.4.
Flood Frequency Analysis
Flood frequency analysis is a tool being widely used for predicting the future flood at different recurrence intervals. The reliable estimates of the magnitude and frequency of occurrence of flood are essential to the proper design of hydraulic structure across a river as well as to identify the flood risk area. Mainly there are two methods of estimating the floods; i.e., deterministic and statistical approach. In the deterministic approach, the rainfall-runoff relationships established based on the physical concepts of the various hydrological processes are used to estimated the floods. In the statistical approach, the past records of flood peaks are subjected to the statistical analysis which provides the distribution pattern for the flood peaks. The frequency analysis is a statistical technique by means of which it is possible to estimate the floods of various magnitudes and their frequencies. The flood frequency analysis for a river site with a long record can be based almost exclusively on the flood record at that site. 3.
Data Requirement
All frequency techniques are totally data dependent. An assumption must be made of a theoretical frequency distribution suitable for the population events and the statistical parameters of the distribution must be computed from the sample data. Two types of sample data, namely (i) annual peak flood series and (ii) partial duration series may be used for flood frequency analysis. Annual peak flood series is arrived at from the recorded flood peaks by picking up only one event from each year of the record. Annual peak flood series ensures complete randomness of the data and thus assumption of randomness is satisfied. But a disadvantage of using this series for analysis is that the second or third highest events in a particular year may be higher than some of the year's annual peak floods and still they are totally disregarded in the analysis. Such a disadvantage is remedied by using the partial duration series in which all the events above a certain threshold are included in the analysis. However care should be taken not to include those peaks which are dependent as the assumption of randomness would be violated. This can be achieved by ensuring that consecutive flood peaks are separated by a recession of a suitable length of time. The procedures for dealing with dependent data are still in research stage. As a preliminary step the basic data should be screened and adjusted to remove, as far as possible, any non-conformity that may exist. The following are the more important considerations (CWC, 1969). •
Effect of man made changes in the regime of flow should be investigated and adjustment be made as required.
•
For small catchments areas a distinction should be made between daily maxima and instantaneous or momentary, flood peaks.
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•
Changes in the stage discharge relation render stage records non homogeneous and unsuitable for frequency analysis studies. It is therefore preferable to work with discharges and if stage frequencies are required, refer the results to the most recent rating.
•
Any useful information contained in data publications and manuscripts should be made use of after proper scrutiny.
The records used for the frequency analysis should satisfy certain assumptions in order to have meaningful estimates; •
Data should be random
•
Data considered for analysis should be homogeneous
•
Data should be of good quality
•
Data should be representative of the population
•
Sample of data should be long enough to provide reliable estimates of the parameters.
4.
Description of Study Area
The Krishna basin for which sufficient annual peak flood series at number of gauging station were available was selected as the study area. The total catchments area of the basin considered for the analysis is 90,000 sq.km and is located between longitude of 73°E to 72°E and latitude of 15°N to 19°N and it comprises the part of Maharashtra and Karnataka states. The figure 1 shows the river system and gauging stations with all its tributary of river Krishna. The drainage area of these gauging sites varies from 540 sq.km to 70,000 sq.km. The main tributaries of river Krishna are river Bhima, Ghataprabha, Malaprabha and Tunga-Bhadra. The TungaBhadra basin which forms a part of the Krishna basin has not been included in the study. 5.
Methodology
The method used in the present study to carry out the regional flood frequency analysis involves the USGS method. The USGS method for estimating the floods of given recurrence intervals for ungauged catchments consists of following sequential steps: •
Select gauged catchments within region having more or less similar hydrological characteristics to that of the ungauged catchments.
•
Establish flood frequency curves for each gauging station using EV-I distribution probability paper.
•
Estimate mean annual flood Q2.33 at each gauging station.
•
Test the homogeneity for gauged catchments.
•
Rank ratios of selected return period floods to the mean annual flood at each station, and
•
Compute median flood ratio for each of the selected return period of step (5), multiply by the estimated mean annual flood of the ungauged catchment’s and plot them against recurrence interval on Gumble probability paper.
•
The end result of these 6th steps is a flood frequency curve for an ungauged catchment’s.
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Fig. 1.
6.
Location Map of Study Area Showing CWC Drainage Basins and River Network
Results and Discussions Table 1.
Preliminary Statistics
Huvinhedgi Galgali Kurundwad Arjunwad Karad
Krishna Krishna Krishna Krishna Krishna
55150 22560 15190 12660 5462
5955.613 6134.493 4257.826 3563.538 2555.545
2228.376 2556.943 1342.008 1677.299 1529.461
Coefficient of Variation 0.374 0.417 0.315 0.421 0.599
Yadgir Takli Narsingpur Dhond Boriomerga Wadakbal Kokangaon Shirdhon Sarati Jewangi Cholachguda Bagalkot Gokak Falls Daddi Gotur Bastewade Terwad Warunji Koyna Nagar
Bhima Bhima Bhima Bhima Borinala Sina Bornala Doddahalla Nira Kagna Malaprabha Ghataprabha Ghataprabha Ghataprabha Hiranyakeshi Vedganga Panchganga Koyna Koyna
69863 33916 22856 11660 2640 12092 1640 630 7200 1920 9373 8610 2776 1150 1100 640 2425 1690 920
3681.1 2930. 618 2635.612 3960.32 370.809 724.55 111.025 39.857 972.5 422.94 1081.9 1097.62 1350.569 1082.15 746.213 604.159 1564.22 1547.382 989.28
2935.770 2565.100 2168.210 3505.076 492.591 748.690 100.420 40.860 724.480 357.960 569.890 897.790 1648.960 460.970 396.200 169.940 442.440 856.230 940.340
0.798 0.875 0.823 0.880 1.328 1.033 0.905 1.150 0.745 0.846 0.527 0.817 1.220 0.426 0.531 0.281 0.283 0.553 0.950
Station name
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Stream
Catchment Area km2
Mean m3/sec
Standard Deviation
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Coefficient of Skewness 0.143 1.633 0.342 0.522 0.833 1.310 0.709 0.857 1.330 1.441 1.733 0.617 1.744 0.192 0.903 1.005 1.680 2.630 1.010 1.216 0.009 0.413 0.860 0.910
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Akshay R. Thorvat et al. / International Journal of Engineering Science and Technology (IJEST) Table 2.
Station Name Huvinhedgi Galgali Kurundwad Arjunwad Karad Yadgir Takli Narsingpur Dhond Boriomerga Wadakbal Kokangaon Shirdhon Sarati Jewangi Cholachguda Bagalkot Gokak Falls Daddi Gotur Bastewade Terwad Warunji Koyna Nagar
Stream
Regression Equations
Krishna Krishna Krishna Krishna Krishna Bhima Bhima Bhima Bhima Borinala Sina Bornala Doddahalla Nira Kagna Malaprabha Ghataprabha Ghataprabha Ghataprabha Hiranyakeshi Vedganga Panchganga Koyna Koyna
QT = 5023.71+1675.76 YT QT = 5042.48+ 1980.34 YT QT =3668.5+ 1059.75 YT QT =2834.2 + 1311.51 YT QT =1873.12 + 1226.31 YT QT =2399.47+ 2304.57 YT QT =1812.07 + 2011.38 YT QT =1670.86 + 1734.83 YT QT =2470.79+ 2678.5 YT QT =172.91 + 355.86 YT QT =415.45 + 555.83 YT QT =66.6 + 79.3 YT QT =21.25 + 33.45 YT QT =665.14 + 552.72 YT QT =264.2 + 285.45 YT QT =826.12 + 459.94 YT QT =1093.21 + 994.24 YT QT =737.36 + 1102.68 YT QT =882.85 + 358.39 YT QT =573.04 + 311.40 YT QT =537.58 + 119.72 YT QT =1384.96 + 322.368 YT QT =1172.27+ 674.53 YT QT =598.33+ 703.0 YT
Table 3.
Regional FF Curve Takali Sr No. Return Period 1 2 3 4 5 6 7
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5 10 20 50 100 200 500
Regression Equations and Mean Annual Flood
Mean Annual Flood Q2.33 5928.1642 4662.3043 4284.5058 3623.1202 2498.9459 3551.0472 2830.4004 2554.53028 3824.6316 360.2595 701.8341 106.9816 38.6768 936.8976 408.3792 1047.581 839.9728 1308.2718 1037.1612 716.569 577.1416 585.058 1489.8756 959.089
Calculation for Absolute Error for Test Site Takali
Estimated Actual Parameter 4829.019 6338.414 7786.261 9660.351 11064.718 12463.961 14309.995
Index Flood Method QT/Q2.33 =0.6970 + 0.5220 YT QT =1812.07 + 2011.38 YT Estimated Absolute Difference Regression Site-1 Site-2 Parameter 4223.577 5341.487 6413.814 7801.831 8841.954 9878.282 11245.520
605.442 420.681 996.926 763.262 1372.447 1091.873 1858.521 1517.228 2222.764 1835.971 2585.679 2153.551 3064.475 2572.537 Sum Average
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Absolute Error Site-1
Site-2
0.125 0.157 0.176 0.192 0.201 0.207 0.214 1.2738 0.1819
0.087 0.120 0.140 0.157 0.166 0.173 0.180. 1.0233 0.1460
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Akshay R. Thorvat et al. / International Journal of Engineering Science and Technology (IJEST) Table 4.
Regional FF Curve Gotur Sr No. Return Period
1 2 3 4 5 6 7
5 10 20 50 100 200 500
Calculation for Absolute Error for Test Site Gotur
Estimated Actual Parameter 1040.121 1273.804 1497.959 1788.104 2005.526 2222.156 2507.957
Table 5.
751.043 949.832 1140.515 1387.334 1572.291 1756.572 1999.697
Absolute Error
289.078 75.260 323.972 136.800 357.444 195.830 400.769 272.239 433.236 329.497 465.584 386.497 508.260 461.811 Sum Average
Site-1
Site-2
0.278 0.254 0.239 0.224 0.216 0.210 0.203 1.623 0.2312
0.072 0.107 0.131 0.152 0.164 0.174 0.184 0.985 0.1410
Calculation for Relationship between Q2.33 and Catchment Area
Station Name Galgali Arjunwad Karad Yadgir Narsingpur Dhond Boriomerga Wadakbal Kokangaon Shirdhon Sarati Jewangi Cholachguda Bagalkot Gokak Falls Daddi Warunji Koyna Nagar
Index Flood Method QT/Q2.33 =0.6970 + 0.5220 YT QT =573.04 + 311.40 YT Estimated Absolute Difference Regression Site-1 Site-2 Parameter
Q2.33
Catchment Area km2 22560 12660 5462 69863 22856 11660 2640 12092 1640 630 7200 1920 9373 8610 2776 1150 1690 920
ln Q2.33
ln A
6191.077 3594.876 2584.380 3736.121 2677.061 4024.320 379.309 737.831 112.594 40.651 985.718 429.761 1092.885 1669.869 1376.914 1090.716 1563.497 1006.070 Sum Mean Standard Deviation Constants in Regression Equation
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8.731 10.024 8.187 9.446 7.857 8.606 8.226 11.154 7.892 10.037 8.300 9.364 5.938 7.879 6.604 9.400 4.724 7.402 3.705 6.446 6.893 8.882 6.063 7.560 6.997 9.146 7.421 9.061 7.228 7.929 6.995 7.048 7.355 7.432 6.914 6.824 126.029 153.639 7.002 8.536 1.277 1.286 0.5037 2.7020 ln Q2.33 = 2.7020 + 0.5037 ln A Q2.33 = 14.9095 A 0.5037
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7.
Conclusion •
Four sites namely Huvinhedgi, Kurundwad, Bastewade and Terwad are not in homogeneity area.
•
The Regional Flood Frequency curve for upper Krishna Basin is: QT/Q2.33= 0.6970+ 0.5220 YT
•
The relationship between Q2.33 and the area for upper Krishna basin is: Q2.33= 14.9095.A0.5037
8.
•
The absolute errors in flood prediction using atsite parameter & atsite mean are 14.10 % and 14.60 % for Gotur and Takali respectively.
•
The absolute errors in flood prediction using regional parameter and regional mean are 23.12 % and 18.19 % for Gotur and Takali respectively.
•
Further research is necessary to improve regional mean values. The regional mean value largely depends on catchment area. However Q2.33 dependent on other catchment characteristics such as drainage density, average elevation of catchment, average slope of stream and catchment, average annual rainfall, land use and land cover etc. should be tried for further improvements. References
[1]
B. N. S. Chalam, M. Krishnaveni, M. Karmegam (1996), “Correlation Analysis of Runoff with Geomorphic Parameters”, Journal of Applied Hydrology, Vol. IX, No.3, 4 1996, 24-31. [2] Burn, D.H. (1990), “Evaluation of regional flood frequency analysis with a region of influence approach”, Water Resour. Res.”, 26(10), 2257 – 2265. [3] Central Water and Power Commission (1969), ‘Estimation of Design Flood-Recommended Procedure’. [4] Cunnane, C. (1988), “Methods and merits of regional flood frequency analysis.” J. Hydrol., 100, 269 – 290. [5] Dalrymple T. (1960), “Flood frequency methods”, U. S. Geol. Surv. Water supply pap, 1543A, U.S. Govt. Printing office, Washington, D.C., 11 – 51. [6] G. Bhaskaran, R. Jayakumar, J. Moses Edwin, K. Kumaraswamy, “Identification of Influential Geomorphic Parameters in Hydrological Modelling through Numerical Analysis”, Journal of Applied Hydrology, Vol. XV, No. 1, 1-8. [7] Hosking, J.R.M, Wallis, J.R. (1990), Regional Flood Frequency Analysis, IBM Research Report. [8] Hosking, J.R.M, Wallis, J.R. (1993), “Some statistics useful in regional frequency analysis” Water Resour. Res., 29(2), 271 -281 [9] Lim, Y.H., Lye, L.M. (2003), “Regional flood estimation for ungauged basins in Sarwak, Malaysia”, Hydrological Sci. J., 48 (1), 7993 [10] National Institute of Hydrology, Roorkee, “Flood Frequency Analysis” Lecture notes. [11] Seth, S.M., Kumar, R., Singh, R.D. (1995), “Development of regional flood formula for Mahanadi sub zone, 3(d)” NIH Technical Report, TR (BR )- 134. [12] Seth, S. M., Mishra, G.C., Venkatesh, B., Singh, R.D. (1997), “Development of regional flood formula for Krishna basin”, NIH Report, CS (AR)-39.
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