TECHNICAL PAPERS
Feb 21, 2009

Adequacy of Nakagami- m Distribution Function to Derive GIUH

Publication: Journal of Hydrologic Engineering
Volume 14, Issue 10

Abstract

Nash and Clark based geomorphological instanteneous unit hydrograph (GIUH) approach proved its usefulness to compute the synthetic unit hydrograph (SUH) and in turn the direct surface runoff component for ungauged catchments. In recent development, two-parameter Weibull’s distribution, coupled with Horton’s ratio, was used to derive the SUH. In continuation with these innovations, present study was conducted to test the adequacy of two-parameter Nakagami- m distribution to derive the GIUH along with two-parameter logistic, two-parameter Weibull, and two-parameter gamma distributions (Nash model). Nakagami- m distribution approach was first tested on the published data and then used to develop the GIUH for Bhagirathi-Bhilangana River catchment. Based on the results of comparison with other approaches, it seems that Nakagami- m distribution-based GIUH can be a good substitute to other existing approaches.

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Acknowledgments

The writers thank Dr. R. K. Rai (Water Resources Consultant) and Dr. Alka Upadhyay (Environment Consultant), DHI (India) Water, Environment and Health, New Delhi (India), and Mr. Aniruddha Chandra, M.E (Communication Engineering), Lecturer, NIT Durgapur, West Bengal for their constructive suggestions to improve the quality of the paper. The writers thank the anonymous reviewers for their constructive suggestions to improve the quality of the paper

References

ARC/INFO Window; version 9. (2005). ESRI Inc., Redlands, Calif.
Bhaskar, N. R., Parida, B. P., and Nayak, A. K. (1997). “Flood estimation for ungauged catchments using the GIUH.” J. Water Resour. Plann. Manage., 123(4), 228–238.
Bhunya, P. K., Berndtsson, R., Singh, P. K., and Hubert, P. (2008). “Comparison between Weibull and gamma distributions to derive synthetic unit hydrograph using Horton ratios.” Water Resour. Res., 44, W04421.
Bras, R. L. (1990). Hydrology: An introduction to hydrologic science, Addison-Wesley, Reading, Mass.
Central Water Commission Research Designs (CWC). (1994). “Directorate of Hydrology (Regional Studies) and India Meteorological Dept. and Ministry of Surface Transport Flood Estimation Report for Western Himalayas—Zone 7.” Rep. No. WH/22/1994, CWC, New Delhi, India.
Charash, U. (1979). “Reception through Nakagami eading multipath channels with random delays.” IEEE Trans. Commun., 27(4), 657–670.
Chow, V. T. (1964). Hand book of applied hydrology, McGraw-Hill, New York.
Clark, C. O. (1945). “Storage and the unit hydrograph.” Trans. Am. Soc. Civ. Eng., 110, 1419–1446.
ERDAS IMAGINE; version 8.6. (2002). ERDAS LLC, Norcross, Ga.
GLCF. (2008). “Earth science data interface.” ⟨http://glcfapp.umiacs. umd.edu:8080/esdi/index.jsp⟩ (January 2008).
Gregory, K. J., and Walling, D. E. (1973). Drainage basin form and process: A geomorphologic approach, Wiley, New York, 456.
Gupta, V. K., Waymire, E., and Wang, C. T. (1980). “Representation of an instantaneous unit hydrograph from geomorphology.” Water Resour. Res., 16(5), 855–862.
Hadley, R. F., and Schumm, S. A. (1961). “Sediment sources and drainage basin characteristics in upper Cheyenne River Basin.” USGS Water Supply Paper No. 1531-B, 198.
Horton, R. E. (1932). “Drainage basin characteristics.” EOS Trans. Am. Geophys. Union, 13, 350–361.
Horton, R. E. (1945). “Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology.” Geol. Soc. Am. Bull., 56(3), 275–370.
Jarvis, A., Reuter, H. I., Nelson, A., and Guevara, E. (2008). “Hole-filled seamless SRTM data V4.” International Center for Tropical Agriculture (CIAT), ⟨http://srtm.csi.cgiar.org⟩ (February 2008).
Karagiannidis, G. K., Zogas, D. A., and Kotsopoulos, S. A. (2003). “On the multivariate Nakagami- m distribution with exponential correlation.” IEEE Trans. Commun., 51(8), 1240–1244.
Kumar, R., Chatterjee, C., Lohani, A. K., Kumar, S., and Singh, R. D. (2002). “Sensitivity analysis of the GIUH-based Clark model for a catchment.” Water Resour. Manage., 16, 263–278.
Kumar, R., Chatterjee, C., Singh, R. D., Lohani, A. K., and Kumar, S. (2007). “Runoff estimation for an ungauged catchment using geomorphologic instantaneous unit hydrograph (GIUH) model.” Hydrolog. Process., 21, 1829–1840.
Maidment, D. R. (1993). Handbook of applied hydrology, McGraw-Hill, New York.
Mesa, L. M. (2006). “Morphometric analysis of a subtropical Andean basin.” Environ. Geol., 50, 1235–1242.
Messa, O. J., and Mifflin, E. R. (1986). “On the relative role of hillslope and network geometry in hydrologic response.” Scale problems in hydrology, V. Gupta, I. Rodriguez-Iturbe, and E. Wood, eds., Reidel, Dordrecht, Holland.
Miller, V. C. (1953). “A quantitative geomorphic study of drainage basin characteristics in the Clinch Mountain area, Virginia, and Tennessee.” Technical Rep. Prepared for Office of Naval Research, Columbia Univ., New York.
Nakagami, M. (1960). “The m -distribution—A general formula of intensity of rapid fading.” Statistical Methods in Radio Wave Propagation: Proc., Symp., W. C. Hoffman, ed., Permagon, U.K., 3–36.
Nash, J. E. (1957). “The forms of instantaneous unit hydrograph.” Int. Assoc. Sci. Hydrol. Publ., 45(3), 114–121.
Pakhmode, V., Kulkarni, H., and Deolankar, S. B. (2003). “Hydrological-drainage analysis in watershed-program planning: A case from the Deccan basalt, India.” Hydrogeol. J., 11, 595–604.
Rai, R. K., Sarkar, S., and Gundekar, H. G. (2008a). “Adequacy of two-parameter beta distribution for deriving the unit hydrograph.” Stochastic Hydrol. Hydraul., 39(3), 201–208.
Rai, R. K., Sarkar, S., and Singh, V. P. (2008b). “Evaluation of the adequacy of statistical distribution functions for deriving unit hydrograph.” Water Resour. Manage., 23, 899–929.
Rai, R. K., and Upadhyay, A. (2008). “Geomorphometric investigation and Nash-based GIUH for Gomti River basin of India.” UPID, Lucknow, India.
Reddy, G. P. O., Maji, A. K., and Gajbhiye, K. S. (2004). “Drainage morphometry and its influence on landform characteristics in a basaltic terrain, Central India—A remote sensing and GIS approach.” Int. J. Appl. Earth Obs. Geoinf., 6(1), 1–16.
Rodriguez-Iturbe, I., Gonzalas, S. M., and Bras, R. C. (1982). “The geomorphoclimatic theory of the instantaneous unit hydrograph.” Water Resour. Res., 18(4), 877–886.
Rodriguez-Iturbe, I., and Valdes, J. B. (1979). “The geomorphologic structure of hydrologic response.” Water Resour. Res., 15(6), 1409–1420.
Rosso, R. (1984). “Nash model relation to Horton order ratios.” Water Resour. Res., 20, 914–920.
Singh, V. P. (1988). Elementary hydrology, Prentice-Hall, New York.
Smith, K. G. (1950). “Standards for grading texture of erosional topography.” Am. J. Sci., 248, 655–668.
Strahler, A. N. (1952). “Dynamic basis for geomorphology.” Bull. Geol. Soc. Am., 63, 923–938.
Strahler, A. N. (1957). “Quantitative analysis of watershed geomorphology.” Trans. Am. Geophys. Union, 38, 913–920.
Strahler, A. N. (1964). “Quantitative geomorphology of drainage basin and channel networks.” Handbook of applied hydrology, V. T. Chow, ed., McGraw-Hill, New York, 4–76.
Subramanya, K. (2003). Engineering hydrology, McGraw-Hill, New York.
Van der Tak, L. D. (1988). “Part 1: Stream length distributions, hillslope effects and other refinements of the other geomorphologic IUH. Part II: Topologically random channel networks and Horton’s laws: The Howard network simulation model revisited.” Civil Engineer thesis, MIT, Cambridge, Mass.
Wisler, C. O., and Brater, E. F. (1959). Hydrology, Wiley, London, 408.
Wyss, J. (1988). “Hydrologic modeling of New England river basins using radar rainfall data.” MS thesis, MIT, Cambridge, Mass.
Zelazinski, J. (1986). “Application of the geomorphological instantaneous unit hydrograph theory to development of forecasting models in Poland.” Hydrol. Sci. J., 31, 2–6.

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Published In

Go to Journal of Hydrologic Engineering
Journal of Hydrologic Engineering
Volume 14Issue 10October 2009
Pages: 1070 - 1079

History

Received: Sep 3, 2008
Accepted: Feb 19, 2009
Published online: Feb 21, 2009
Published in print: Oct 2009

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Authors

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Research Scholar, Dept. of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India (corresponding author). E-mail: [email protected]
Professor, Dept. of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India. E-mail: [email protected]
B. S. Mathur
Emeritus Fellow and Retired Professor, Dept. of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India.

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