Abstract
A design hyetograph represents the temporal distribution of rainfall intensity associated with a return period. The choice of the design hyetograph will have a significant influence on the shape and peak value of the hydrograph. Hence, the determination of design hyetographs is an important task in the hydrologic designs. In this paper, an approach is proposed to develop design hyetographs for ungauged sites. The proposed approach is composed of four steps: principal component analysis (PCA), self-organizing map (SOM)-based clustering, region delineation, and kriging-based construction. Firstly, PCA is applied to obtain the principal components of the design hyetographs. Then the transformed data resulting from PCA and the three geographic characters of the gauges are used as input data to the SOM, which is applied to group the rain gauges into specific clusters. Thirdly, the regions for these clusters are delineated and then the regions map is made. Finally, the design hyetographs for ungauged sites is constructed by using the kriging method. The proposed approach is applied to estimate the design hyetographs of ungauged sites in Taiwan. For comparison with the proposed approach, three other approaches are executed. Four gauges are treated as ungauged and the three approaches are used to construct the design hyetographs. The results show that accurate estimated design hyetographs can be obtained by the proposed approach. Cross-validation tests further have been performed to examine the stability and the accuracy of these approaches. Again, the results indicate that the proposed approach is more accurate and stable than the other approaches. Overall, the results demonstrate that the proposed approach is useful to develop design hyetographs for ungauged sites.
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References
Arnaud P, Lavabre J, Sol B, Desouches C (2008) Regionalization of an hourly rainfall generating model over metropolitan France for flood hazard estimation. Hydrol Sci J 53(1):34–47
ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000a) Artificial neural networks in hydrology. I: preliminary concepts. J Hydrol Eng-ASCE 5(2):115–123
ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000b) Artificial neural networks in hydrology. II: hydrologic applications. J Hydrol Eng-ASCE 5(2):124–137
Bowden GJ, Maier HR, Dandy GC (2002) Optimal division of data for neural network models in water resources applications. Water Resour Res 38(2):1010. doi:10.1029/2001WR000266
Bowden GJ, Dandy GC, Maier HR (2005a) Input determination for neural network models in water resources applications. Part 1—background and methodology. J Hydrol 301:75–92
Bowden GJ, Maier HR, Dandy GC (2005b) Input determination for neural network models in water resources applications. Part 2—case study: forecasting salinity in a river. J Hydrol 301:93–107
Cereghino R, Giraudel JL, Compin A (2001) Spatial analysis of stream invertebrates distribution in the Adour–Garonne drainage basin (France), using Kohonen self-organizing maps. Ecol Model 146:167–180
Cheng KS, Lin GF, Wang RY, Hsu MH, Yu GH, Yu PS, Lee KT (2001a) Handbook for hydrological design. Technical Report, Water Resources Agency, Ministry of Economic Affairs, Taipei, Taiwan (in Chinese)
Cheng KS, Hueter I, Hsu EC, Yen HC (2001b) A scale-invariant Gauss–Markov model for design storm hyetographs. J Am Water Resour Assoc 37(3):723–735
Chiang SM, Tsay TK, Nix SJ (2002) Hydrologic regionalization of watersheds. I: methodology development. J Water Resour Plan Manage-ASCE 128(1):3–11
Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York
Hancock JR (1993) Multivariate regionalization: an approach using interactive statistical visualization. Auto-Carto-11, Minneapolis, pp 218–227
Haykin S (1994) Neural networks: a comprehensive foundation. IEEE, New York
Hong Y, Hsu K, Sorooshian S, Gao X (2005) Self-organizing nonlinear output (SONO): a neural network suitable for cloud patch-based rainfall estimation at small scales. Water Resour Res 41:W03008. doi:10.1029/2004WR003142
Hsu K, Gupta HV, Gao X, Sorooshian S, Imam B (2002) Self-organizing linear output map (SOLO): an artificial neural network suitable for hydrologic modeling and analysis. Water Resour Res 38(12):1302. doi:10.1029/2001WR000795
Kalteh AM, Berndtsson R (2007) Interpolating monthly precipitation by self-organizing map (SOM) and multilayer perceptron (MLP). Hydrol Sci J 52(2):305–317
Kalteh AM, Hjorth P, Berndtsson R (2008) Review of the self-organizing map (SOM) approach in water resources: analysis, modelling and application. Environ Model Softw 23(7):835–845
Kohonen T (1982a) Analysis of a simple self-organizing process. Biol Cybern 44:135–140
Kohonen T (1982b) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69
Kohonen T (2001) Self-organizing maps, 3rd edn. Springer, Berlin
Kysely J, Picek J, Huth R (2007) Formation of homogeneous regions for regional frequency analysis of extreme precipitation events in the Czech Republic. Stud Geophys Geod 51(2):327–344
Lin GF, Wang CM (2006) Performing cluster analysis and discrimination analysis of hydrological factors in one step. Adv Water Resour 29(11):1573–1585. doi:10.1016/j.advwatres.2005.11.008
Lin GF, Wu MC (2007) A SOM-based approach to estimating design hyetographs of ungauged sites. J Hydrol 339(3–4):216–226
Lin GF, Chen LH, Kao SC (2005) Development of regional design hyetographs. Hydrol Process 19(4):937–946
Lin GF, Wu MC, Chen GR, Liu SJ (2010) Construction of design hyetographs for locations without observed data. Hydrol Process 24(4):481–491
Meshgi A, Khalili D (2009) Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. I. A re-visit to regional homogeneity. Stoch Environ Res Risk Assess 23(1):119–135
Pinault JL, Allier D (2007) Regionalization of rainfall for broad-scale modeling: an inverse approach. Water Resour Res 43(9):W09422. doi:10.1029/2006WR005642
Rao AR, Srinivas VV (2006a) Regionalization of watersheds by fuzzy cluster analysis. J Hydrol 318(1–4):57–79
Rao AR, Srinivas VV (2006b) Regionalization of watersheds by hybrid-cluster analysis. J Hydrol 318(1–4):37–56
Satyanarayana P, Srinivas VV (2008) Regional frequency analysis of precipitation using large-scale atmospheric variables. J Geophys Res-Atmospheres 113:D24110. doi:10.1029/2008JD010412
Schutze N, Schmitz GH, Petersohn U (2005) Self-organizing maps with multiple input–output option for modeling the Richards equation and its inverse solution. Water Resour Res 41:W03022. doi:10.1029/2004WR003630
Shanmuganathan S, Sallis P, Buckeridge J (2006) Self-organising map methods in integrated modelling of environmental and economic systems. Environ Model Softw 21:1247–1256
Trakhtenbrot A, Kadmon R (2006) Effectiveness of environmental cluster analysis in representing regional species diversity. Conserv Biol 20(4):1087–1098
Tran LT, Knight CG, O’Neill RV, Smith ER, O’Connell M (2003) Self-organizing maps for integrated environmental assessment of the Mid-Atlantic region. Environ Manage 31(6):822–835
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Chen, LH., Lin, GF. & Hsu, CW. Development of Design Hyetographs for Ungauged Sites Using an Approach Combining PCA, SOM and Kriging Methods. Water Resour Manage 25, 1995–2013 (2011). https://doi.org/10.1007/s11269-011-9791-4
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DOI: https://doi.org/10.1007/s11269-011-9791-4