Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A Principal Component Regression Method for Estimating Low Flow Index

  • 343 Accesses

  • 23 Citations

Abstract

Low flow indices are very important for water resources planning, pollution control, conservation and even recreational use. Determining these indices depends on having access to daily flow discharges. However, in some cases, such data are either insufficient or are not available at all. Hence, in these cases, estimation of the indices requires the use of data in catchments for which streamflow data have been collected. In this paper, it was attempted to estimate the low flow index (7Q10), the 7-day, 10-year lowflow, using principal component regression (PCR) based on physiographic and hydrologic variables. To do so, a two-step procedure was followed. In the first step, ranking method was applied to determine the best fitted distributions on yearly minimum discharges in each gauging station according to distribution suitability for fitting on extremes; the better the distribution fits the data, the higher number is given as ranking. Adding the ranking numbers dedicated to each gauging station, it was revealed that Gamma distribution with two parameters got the highest value and therefore was chosen as the representative distribution in the region. Using Gamma distribution in gauging stations, 7Q10 was estimated in all gauging stations in the basin. In the second step, a PCR was developed due to existence of high-correlated independent variables. To choose the influential components for use in PCR, eigenvector analysis and factor analysis were performed. The results show that the components chosen through the two approaches correspond to each other well. To evaluate the efficiency of the developed PCR in modeling 7Q10, calibration and verification were pursued. The results approve the efficiency of model in predicting 7Q10 in the region under study.

This is a preview of subscription content, log in to check access.

References

  1. Amusja AZ,Gutnichenko VG, Shelutko VA (1988) On the estimation of mean annual value of minimum winter flow of ungauged rivers. Trudy GGI (Trans State Hydrol Inst, Leningrad, USSR) 335:43–53

  2. Deksissa T, Ashton PJ, Vanrolleghem PA (2003) Control options for river water quality improvement: a case study of TDS and inorganic nitrogen in the Crocodile River (South Africa). Water SA 29:209–217

  3. Engeland K, Hisdal H (2009) A comparison of low flow estimates in ungauged catchments using regional regression and the HBV-Model. Water Resour Manag J 23:2567–2586

  4. Eslamian S, Biabanaki M (2008) Low flow regionalization modeling. J Ecological Economics and Statistics 12(F08):82–97

  5. Flynn RH (2003) A stream-gaging network analysis for the 7-day, 10-year annual low flow in New Hampshire streams. USGS, Pembroke

  6. Gunst RF, Mason RL (1980) Regression analysis and its applications: a data-oriented approach. Dekker, New York

  7. Gustard A, Bullock A, Dixon JM (1992) Low flow estimation in the United Kingdom. Institute of Hydrology, Wallingford, Report No. 108, 88 pp, append

  8. Gustard A, Irving KM (1994) Classification of the low flow response of European soils. FRIEND: Flow Regimes from International Experimental and Network Data. IAHS, Idyllwild, pp 113–117

  9. Harman HH (1960) Modern factor analysis. University of Chicago press, Chicago

  10. Hocking RR, Speed FM, Lynn MJ (1976) A class of biased estimators in linear regression. Technometrics 18:425–437

  11. Imhof JG, Brown D (2003) Guaranteeing environmental flows in Ontario’s rivers and streams. A Position Statement prepared by Trout Unlimited Canada & Ontario Federation of Anglers and Hunters, 7 p

  12. Jolliffe IT (2002) Principal component analysis. Principal components in regression analysis, 2nd edn. Springer, New York, pp 167–198

  13. Jolliffe IT, Jones B, Morgan BJT (1982) Utilising clusters: a case study involving the elderly. J R Stat Soc A 145:224–236

  14. Kirk A, McCuen RH (2008) Outlier detection in multivariate hydrologic data. J Hydrol Eng 13:7(6410)

  15. Kroll C, Luz J, Allen B, Vogel R (2004) Developing a watershed characteristics database to improve low streamflow prediction. J Hydrol Eng 9(2):116–125

  16. Mansfield ER, Webster JT, Gunst RF (1977) An analytic variable selection technique for principal component regression. Appl Stat 26:34–40

  17. Mhango DHZ, Joy DM (1998) Low flow characteristics and assessment of domestic water abstraction permits in Malawi. In: Proceedings conference on hydrology in a changing environment, Exeter, UK

  18. Mohamed M, Stednick JD, Smith FM (2002) Comparison of field measurements to predicted reaeration coefficients, k2, in the application of a water quality model, QUAL2E, to a tropical river. Water Sci Technol 46:47–54

  19. Montgomery DC, Peck EA, Vining GG (2001) Introduction to linear regression analysis. Wiley, New York, pp 117–317

  20. Rifai HS, Suzanne MB, Ensor KB, Bedient PE (2000) Determination of low-flow characteristics for Texas streams. J Water Res Plan Manage 126(5):310–331

  21. Rosner B (1983) Percentage points for a generalized ESD many outlier procedure. Technometrics 24:165–172

  22. Schreiber P, Demuth S (1997) Regionalisation of low flows in southwest Germany. Hydrol Sci J 42(6):845–858

  23. Skop E, Loaiciga HA (1998) Investigating catchment hydrology and low-flow characteristics using GIS. Nordic Hydrol 29(2):105–128

  24. Smakhtin VU (2001) Low flow hydrology: a review. J Hydrol 240:147–186.9

  25. Smakhtin VU, Watkins DA, Hughes DA (1995) Preminilary analysis of low-flow characteristics of South African rivers. Water SA 21(3):201–210

  26. Spencer CS, McCuen RH (1996) Detection of outliers in Pearson type III data. J Hydrol Eng 1:2–10

  27. Vogel RM, Kroll CN (1990) Generalized low-flow frequency relationships for ungauged sites in Massachusetts. Water Resour Bull 26(2):241–253

  28. Wallace TB, Cox WE (2002) Locating information on surface water availability in Virginia (draft). Accessed: March 2004. http://www.rappriverbasin.state.va.us/studies, 24 p

Download references

Author information

Correspondence to Mehdi Ghasemizadeh.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Eslamian, S., Ghasemizadeh, M., Biabanaki, M. et al. A Principal Component Regression Method for Estimating Low Flow Index. Water Resour Manage 24, 2553–2566 (2010). https://doi.org/10.1007/s11269-009-9567-2

Download citation

Keywords

  • Low flow
  • Principal component regression
  • Factor analysis
  • Eigenvector