Low flow frequency analysis by L-moments method (Case study: Iranian Central Plateau River Basin)

Document Type: Research Paper

Author

Desert management Dept., International Desert Research Center (IDRC), University of Tehran

Abstract

Knowledge about low flow statistics is essential for effective water resource planning and management in ungauged or
poorly gauged catchment areas, especially in arid and semi-arid regions such as Iran. We employed a data set of 20 river
flow time-series from the Iranian Central Plateau River Basin, Iran to evaluate the low-flow series using several frequency
analysis methods and compared the result of these methods in their ability to set low flows for the conservation of
instream water uses. Theoretical frequency distributions including the log-normal, three-parameter lognormal, Gumbel,
Pearson type III, and log Pearson type III were applied with the low-flow series. Goodness-of-fit tests including Lmoment
and conventional moment methods for the observed data were applied to identify the best distributions. For each
distribution, the calculated values of the residual sum of squares (RSS) was applied to compare between the conventional
moment and L-moment methods, and the best method was selected to determine the most appropriate probability
distribution. The lowest RSS values were used to select the best distribution for each station. Then, T-year low-flow series
was estimated using the best probability distribution. Our results suggested that, for annual low flows, based on the
computed RSS, Pearson type III, log Pearson type III, Gumbel distributions, and L-moment method were suitably
distinguished for 85%, 10%, and 5% of the stations, respectively. Finally, Compared to the conventional moment method,
L-moments method was found to be more adequate to identify low-flow series probability distributions in the Iranian
Central Plateau River Basin, while Pearson type III was found to be the best probability distribution for modeling
minimum flow series in the study area.

Keywords


Bayazit, M., B. Önoz, 2002. LL-moments for estimating
low flow quantiles / Estimation des quantiles d'étiage
grâce aux LL-moments. Hydrological Sciences Journal,
47; 707-720.
Caruso, B.S., 2000. Evaluation of low-flow frequency
analysis methods. Journal of Hydrology (NZ), 39; 19-
47.
Chen, Y.D., G. Huang, Q. Shao, C. Xu, 2006. Regional
analysis of low flow using L-moments for Dongjiang
basin, South China. Hydrological Sciences Journal, 51;
1051-1064.
Chowdhury, J.U., J.R. Stedinger, L. Lu, 1991. Goodnessof-
fit tests for regional GEV flood distributions. Water
Resource Research, 27; 1756-1776.
Daviau, J.L., K. Adamowski, G.G. Patry, 2000. Regional
flood frequency anaysis using GIS, L-moment and
geostatistical methods. Hydrological Processes, 14;
2731-2753.
Delleur, J.W., A.R. Rao, J.M. Bell, 1988. Criteria for the
determination of minimum streamflows. Technical
report CE-HSE-88-6, School of Civil Enginieering,
Purdue University, West Lafayyete, Ind.
Dodangeh, E., S. Soltani, A. Sarhadi, J.T. Shiau, 2013.
Application of L-moments and Bayesian inference for
low-flow regionalization in Sefidroud basin, Iran.
Hydrological Processes, 35; 1-14.
Du, T., L. Xiong, Ch.Y. Xu, Ch.J. Gippel, S. Guo, P. Liu,
2015. Return period and risk analysis of nonstationary
low-flow series under climate change. Journal of
Hydrology, 527; 234–250.
Eslamian, S.S., S. Chavoshi, 2003. The Application of Lmoments
Theory in Flood Frequency Analysis of
Central Catchments of Iran. JWSS, 7; 1-17.
Eslamian, S.S., H. Feizi, 2007. Maximum monthly rainfall
analysis using L-moments for an arid region in Isfahan
province, Iran. Journal of Applied Meteorological and
Climatology, 46; 494-503.
Greenwood, J.A., J.M. Landwehr, N.C. Matalas, J.R.
Wallis, 1979. Probability Weighted Moments:
Definitions and Relation to Parameters of Several
Distributions Expressible in Inverse Form. Water
Resource Research, 15; 1049-1054.
Gustard, A., Young, A.E., Rees, G., Holmes, M., 2004.
Low flows, drought and operational hydrology. In:
Tallaksen, L.M., van Lanen, H.A.J. (Eds.), Hydrological
Drought: Processes and Estimation Methods for
Streamflow and Groundwater Developments in Water
Science, vol. 48. Elsevier, NL.
Hosking, J.R.M., 1990. L-moments: analysis and
estimation of distributions using linear combinations of
order statistics. Journal of Royal Statistical Society, 52;
105-124.
Hosking, J.R.M., J.R. Wallis, 1993. Some statistics useful
in regional frequency analysis. Water Resource
Research, 29; 271-281.
Hosking, J.R.M., J.R. Wallis, 1997. Regional frequency
analysis: an approach based on L-moments. Cambridge
University Press, Cambridge, UK.
Iran Water Resources Management Company, 2013. Low
flow data of Iranian Central Plateau River Basin.
Jingyi, Z., M.J. Hall, 2004. Regional Flood Frequency
Analysis for the Gan-Ming River Basin in China.
Journal of Hydrology, 296; 98-117.
Keshtkar, A.R., A. Salajegheh, M. Najafi Hajivar, 2012.
Flood flow frequency model selection using L-moment
method in arid and semi-arid regions of Iran. Desert, 17;
41-48.
Khandi, S., H. Kachroo, R.K. Gunasekara, 2000.
Comparison of Annual Maximum Series and Partial
Duration of Homogeneous Regions. Hydrological
Science Journal, 45; 437-447.
Kjeldsen, T.R., J.C. Smithers, R.E. Schulze, 2001.
Regional Flood Frequency Analysis in the KwaZulu-
Natal Province, South Africa, Using the Index-Flood
Method. Journal of Hydrology, 255; 194-211.
Kroll, C.N., Vogel, R.M., 2002. Probability distribution of
low streamflow series. Journal of Hydrological
Engineering, ASCE, 7; 137–146.

Kumar, R., Chatterjee, C., Kumar, S., Lohani, A.K., Singh,
R.D., 2003. Development of regional flood frequency
relationships using L-moments for Middle Ganga Plains
Subzone 1(f) of India. Water Resource Management,
17; 243–257.
Laaha G., G. Bloschi, 2006. A comparison of low flow
regionalisation methods catchment grouping. Journal of
Hydrology, 323; 193–214.
Lim, Y.H., Lye, L.M., 2003. Regional flood estimation for
ungauged basins in Sarawak, Malaysia. Hydrological
Science Journal, 48; 79–94.
Malekinezhad, H., H.P. Nachtnebel, A. Klik, 2011.
Regionalization Approach for Extreme Flood Analysis
Using L-moments. Journal of Agricultural Science and
Technology, 13; 1183-1196.
Matalas, N.C., 1963. Probability distribution of low flows.
Report 434-A, U.S. Geological Survey, Washington,
D.C.
Minocha, V.K., 2003. Discussion of Probability
distribution of low streamflow series by C.N. Kroll &
R.M. Vogel. Journal of Hydrologic Engineering,
ASCE, 8; 297.
McCuen, R.H., 2003. Modeling hydrologic change:
Statistical methods. CRC Press, Florida, 433p.
Modarres, R., 2008. Regional Frequency Distribution Type
of Low Flow in North of Iran by L-moments. Water
Resources Management, 22; 823-841.
Modarres, R. 2009. Regional Dry Spells Frequency
Analysis by L-Moment and Multivariate Analysis.
Water Resources Management, 24; 2365-2380.
Pandey, M.D., Gelder, P.H., Vrijling, J.K., 2001.
Assessment of an L-kurtosis-based criterion for quantile
estimation. Journal of Hydrologic Engineering ASCE,
6; 284–291.
Parida, B.P., Kachroo, R.K., Shrestha, D.B., 1998.
Regional flood frequency analysis of Mahi-Sabarmati
Basin (Subzone 3-a) using index flood procedure with
L-moments. Water Resources Management, 12; 1–12.
Pearson, C.P., 1995. Regional frequency analysis of low
flow in New Zealand rivers. Journal of Hydrology (NZ),
33; 94-122.
Peel, M.C., T.A. McMahon, B.L. Finlayson, 2004.
Continental Differences in the Variability of Annual
Runoff-Update and Reassessment. Journal of
Hydrology, 295; 185-197.
Peng, S., C. Xi, Q. Si-min, Y. Tao, Z. Zhi-cai, M. Jianliang,
2009. Regional Frequency Analysis of Low Flow
Based on L-Moments in Karst Area, Southwest China.
Joint International Convention of 8th IAHS Scientific
Assembly and 37th IAH Congress, Water: A vital
resource under stress – How Science can help,
September 6-12, Hyderabad, India.
Rostami, R., 2013. Regional Flood Frequency Analysis
Based on L-Moment Approach (Case Study West
Azarbayjan Basins). Journal of Civil Engineering and
Urbanism, 3; 107-113.
Salajegheh, A., A.R. Keshtkar, S. Dalfardi, 2008. To study
of the appropriate probability distributions for annual
maximum series using L-moment method in arid and
semi-arid regions of Iran. XIII World Water Congress,
1-4 september, Montpellier, France.
Sarhadi, A., S. Soltani, R. Modares, 2008. Regional
frequency analysis for low flow using L-moment
method in Jiroft region. Iranian Water Research Journal
(In Persian), 3; 45-54.
Sawaske, S.R., D.R. Freyberg, 2014. An analysis of trends
in baseflow recession and low-flows in rain-dominated
coastal streams of the pacific coast. Journal of
Hydrology, 519; 599–610.
Shi, P., X. Chen, S. Qu, Zh. Zhang, J. Ma, 2010. Regional
Frequency Analysis of Low Flow Based on L Moments:
Case Study in Karst Area, Southwest China. Journal of
Hydrologic Engineering, ASCE, 15:370-377.
Smakhtin, V.U., 2001. Low flow hydrology: a review.
Journal of Hydrology, 240; 147–186.
Smithers, J.C., R.E. Schulze, 2000. A Methodology for the
Estimation of Short Duration Design Storms in South’s
Africa Using a Regional Approach Based on Lmoments.
Journal of Hydrology, 241; 42-52.
Staudinger M, J. Seibert, 2014. Predictability of low flow –
An assessment with simulation experiments. Journal of
Hydrology, 519; 1383–1393.
Stedinger, J.R., R.M. Vogel, F. Foufula-Georgiou, 1993.
Frequency Analysis of Extreme Events, In Handbook of
Applied Hydrology, Ch18, Editor-in-chief, D.A.
Maidment, Mc Grow-Hill, Newyork.PP.1-66.
Thomas, B., G. Lishchied, J. Stiedl, O. Dietrich, 2015.
Long term shift of low flows predictors in small
lowland catchments of Northeast Germany. Journal of
Hydrology, 521; 508–519.
Vogel, R.M., C.N. Kroll, 1989. Low flow frequency
analysis using probability plot correlation coefficients.
Journal of Water Resources Planning and Management,
ASCE, 115; 338-357.
Vogel, R.M., N.M. Fennessey, 1993. L-moments diagrams
should replace product moment diagrams. Water
Resource Research, 29; 1745-1752.
Vogel, R.M., W.O. Thomas, T.A. McMahon, 1993. Flood
flow frequency model selection in Southwestern U.S.A.
Journal of Water Resources Planning and management,
ASCE, 119; 353-366.
Vogel, R., I. Wilson, 1996. Probability Distribution of
Annual Maximum, Mean & Minimum Stream Flows in
the United States. Journal of Hydrologic Engineering,
12; 69-76.
Yurekli, K., A. Kurunc, S. Gul, 2005. Frequency Analysis
of Low Flow Series from Çekerek Stream Basin. Tarim
Bilimleri Dergisi, 11; 72-77.