Estimation of the distribution of annual runoff from climatic variables using copulas

Water Resources Research

Volumn 50, Issue 9, 2014, Pages 7134-7152

  Xiong, Lihua ^a   Yu, Kun Xia ^a   Gottschalk, Lars ^a,b  

^a WUHAN UNIVERSITY   (China)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

The annual runoff distributions derived from the approach perform well; The approach can also be used in ungauged watersheds; The approach of deriving annual runoff distributions using copulas is proposed

Indexed keywords

CLIMATE CHANGE; DISTRIBUTION FUNCTIONS; EVAPOTRANSPIRATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; RAIN; RANDOM VARIABLES; WATERSHEDS; PRECIPITATION (METEOROLOGY);

ACCEPTABLE PERFORMANCE; ANNUAL RUNOFF; ANNUAL WATER BALANCE; JOINT PROBABILITY DENSITY FUNCTION; MARGINAL DISTRIBUTION; POTENTIAL EVAPOTRANSPIRATION; RAINFALL-RUNOFF MODELING; UNGAUGED WATERSHED; BUDYKO FORMULAS; CLIMATIC VARIABLES; COPULA METHOD;

RUNOFF;

FREQUENCY ANALYSIS; POTENTIAL EVAPOTRANSPIRATION; PROBABILITY DENSITY FUNCTION; RUNOFF; VINE; WATER BUDGET; ANNUAL VARIATION; CLIMATE CHANGE; ESTIMATION METHOD; EVAPOTRANSPIRATION; MULTIVARIATE ANALYSIS; NUMERICAL MODEL; RAINFALL-RUNOFF MODELING; SPATIAL DISTRIBUTION; WATERSHED;

CHINA;

EID: 84915795116     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2013WR015159     Document Type: Article

References (55)

1. Aas, K., C. Czado, A. Frigessi, and H. Bakken (2009), Pair-copula constructions of multiple dependence, Insur. Math. Econ., 44(2), 182-198, doi:10.1016/j.insmatheco.2007.02.001.
2. Allen, R. G., L. S. Pereira, D. Raes, and M. Smith (1998), Crop evapotranspiration-guidelines for computing crop water requirements, Irrig. Drain. Pap. 56, Food and Agric. Organ. of the U. N., Rome.
3. Andréassian, V., and C. Perrin (2012), On the ambiguous interpretation of the Turc-Budyko nondimensional graph, Water Resour. Res., 48, W10601, doi:10.1029/2012WR012532.
4. Bárdossy, A. (2006), Copula-based geostatistical models for groundwater quality parameters, Water Resour. Res., 42, W11416, doi:10.1029/ 2005WR004754.
5. Bedford, T., and R. M. Cooke (2002), Vine-A new graphical model for dependent random variables, Ann. Stat., 30(4), 1031-1068, doi: 10.1214/aos/1031689016.
6. Benjamin, J. R., and C. A. Cornell (1970), Probability, Statistics and Decision for Civil Engineers, 260 pp., McGraw-Hill, N. Y.
7. Breymann, W., A. Dias, and P. Embrechts (2003), Dependence structures for multivariate high frequency data in finance, Quant. Finan., 1, 1-14, doi:10.1080/713666155.
8. Budyko, M. I. (1974), Climate and Life, translated from Russian by D. H. Miller, Academic, San Diego, Calif.
9. De Michele, C., and G. Salvadori (2002), On the derived flood frequency distribution: Analytical formulation and the influence of antecedent soil moisture condition, J. Hydrol., 262, 245-258, doi:10.1016/S0022-1694(02)00025-2.
10. De Michele, C., and J. Salvadori (2003), A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas, J. Geophys. Res., 108(D2), 4067, doi:10.1029/2002JD002534.
11. Díaz-Granados, M. A., J. B. Valdes, and R. L. Bras (1984), A physically based flood frequency distribution, Water Resour. Res., 20(7), 995-1002, doi:10.1029/WR020i007p00995.
12. Donohue, R. J., M. L. Roderick, and T. R. McVicar (2010), Can dynamic vegetation information improve the accuracy of Budyko's hydrological model?, J. Hydrol., 390, 23-34, doi:10.1016/j.jhydrol.2010.06.025.
13. Dooge, J. C. I. (1992), Sensitivity of runoff to climate change: A Hortonian approach, Bull. Am. Meteorol. Soc., 73(12), 2013-2024.
14. Dupuis, D. (2007), Using copulas in hydrology: Benefits, cautions, and issues, J. Hydrol. Eng., 12(4), 381-393, doi:10.1061/(ASCE)1084-0699(2007)12:4(381).
15. Eagleson, P. S. (1972), Dynamics of flood frequency, Water Resour. Res., 8(4), 878-898, doi:10.1029/WR008i004p00878.
16. Eagleson, P. S. (1978a), Climate, soil, and vegetation 5: A derived distribution of storm surface runoff, Water Resour. Res., 14(5), 741-748, doi:10.1029/WR014i005p00741.
17. Eagleson, P. S. (1978b), Climate, soil, and vegetation 7: A derived distribution of annual water yield, Water Resour. Res., 14(5), 765-776, doi: 10.1029/WR014i005p00765.
18. Favre, A.-C., S. El Adlouni, L. Perreault, N. Thiémonge, and B. Bobee (2004), Multivariate hydrological frequency analysis using copulas, Water Resour. Res., 40, W01101, doi:10.1029/2003WR002456.
19. Fu, B. P. (1981), On the calculation of the evaporation from land surface [in Chinese], Sci. Atmos. Sin., 5, 23-31.
20. Genest, C., and A.-C. Favre (2007), Everything you always wanted to know about copula modeling but were afraid to ask, J. Hydrol. Eng., 12(4), 347-368, doi:10.1061/(ASCE)1084-0699(2007)12:4(347).
21. Gottschalk, L. (2006), Methods for analysing variability, in Encyclopaedia of Hydrological Sciences, vol. 1, edited by M. G. Anderson and J. J. McDonnell, 29 pp., John Wiley, Chichester, U. K.
22. Gottschalk, L., and R. Weingartner (1998), Distribution of peak flow derived from a distribution of rainfall volume and runoff coefficient, and a unit hydrograph, J. Hydrol., 208, 148-162, doi:10.1016/S0022-1694(98)00152-8.
23. Hosking, J. R. M. (1990), L-moments: Analysis and estimation of distributions using linear combinations of order statistics, J. R. Stat. Soc. Ser. B, 52, 105-124.
24. Hosking, J. R. M., and J. R. Wallis (1997), Regional Frequency Analysis, Cambridge Univ. Press, Cambridge, U. K.
25. Hosseinzadeh Talaee, P., H. Tabari, and H. Abghari (2013), Pan evaporation and reference evapotranspiration trends detection in western Iran with consideration of data persistence, Hydrol. Res., 45, 213-225, doi:10.2166/nh.2013.058.
26. Interagency Advisory Committee on Water Data (1982), Guidelines for Determining Flood Flow Frequency, Bulletin 17B of the Hydrology Subcommittee, Off. of Water Data Coord., Reston, Va.
27. Joe, H. (1996), Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters, in Distributions With Fixed Marginals and Related Topics, Lecture Notes-Monogr. Ser., vol. 28, edited by L. Ruschendorf, B. Schweizer, and M. D. Taylor, pp. 120-141, Inst. of Math. Stat., Hayward, Calif., doi:10.1214/lnms/1215452614.
28. Kuhnel, V., J. C. I. Dooge, J. P. J. O'Kane, and R. J. Romanowicz (1991), Partial analysis applied to scale problems in surface moisture fluxes, Surv. Geophys., 12, 221-247, doi:10.1007/BF01903420.
29. Lebecherel, L., V. Andréassian, and C. Perrin (2013), On regionalizing the Turc-Mezentsev water balance formula, Water Resour. Res., 49, 7508-7517, doi:10.1002/2013WR013575.
30. Mezentsev, V. (1955), More on the computation of total evaporation (Yechio raz o rastchetie srednevo summarnovo ispareniia), Meteorol. Gidrol., 5, 24-26.
31. Nelsen, R. B. (2006), An Introduction to Copulas, 2nd ed., Springer, N. Y.
32. Ol'dekop, E. M. (1911), On evaporation from the surface of river basins, in Transactions on Meteorological Observations, Univ. of Tartu, Tartu, Estonia.
33. Pike, J. G. (1964), The estimation of annual runoff from meteorological data in a tropical climate, J. Hydrol., 2, 116-123.
34. Qin, D., et al. (2006), Assessment of climate and environment changes in China (I): Climate and environment changes in China and their projections, Adv. Clim. Change Res., 2, 1-5.
35. Rosenblatt, M. (1952), Remarks on multivariate transformation, Ann. Math. Statist., 23, 1052-1057, doi:10.1214/aoms/1177729394.
36. Robson, A. J., and D. W. Reed (1999), Flood Estimation Handbook, Institute of Hydrology, Wallingford, U. K.
37. Salvadori, G., and C. De Michele (2004), Frequency analysis via copulas: Theoretical aspects and applications to hydrological events, Water Resour. Res., 40, W12511, doi:10.1029/2004WR003133.
38. Salvadori, G., and C. De Michele (2007), On the use of copulas in hydrology: Theory and practice, J. Hydrol. Eng., 12(4), 369-380, doi: 10.1061/(ASCE)1084-0699(2007)12:4(369).
39. Schreiber, P. (1904), Über die Beziehungen zwischen dem Niederschlag und der Wasserführung der Flüsse in Mitteleuropa, Z. Meteorol., 21, 441-452.
40. Sivapalan, M., E. F. Wood, and K. Beven (1990), On hydrologic similarity 3: A dimensionless flood frequency model using a generalized geomorphologic unit hydrograph and partial area runoff generation, Water Resour. Res., 26(1), 43-58, doi:10.1029/WR026i001p00043.
41. Sivapalan, M., G., Blöschl, R. Merz, and D. Gutknecht (2005), Linking flood frequency to long-term water balance: Incorporating effects of seasonality, Water Resour. Res., 41, W06012, doi:10.1029/2004WR003439.
42. Tabari, H., J. Nikbakht, and P. Hosseinzadeh Talaee (2012), Identification of trend in reference evapotranspiration series with serial dependence in Iran, Water Resour. Manage., 26, 2219-2232, doi:10.1007/s11269-012-0011-7.
43. Teng, J., F. H. S. Chiew, J. Vaze, S. Marvanek, and D. G. C. Kirono (2012), Estimation of climate change impact on mean annual runoff across continental Australia using Budyko and Fu equations and hydrological Models, J. Hydrometeorol., 13, 1094-1106, doi:10.1175/JHM-D-11-097.1.
44. Turc, L. (1954), Le bilan d'eau des sols: Relation entre les précipitations, l'évaporation et l'écoulement, Ann. Agron., Ser. A, 5, 491-595.
45. U.S. Army Corps of Engineers (1994), Engineering and design: Flood-runoff analysis, Rep. EM 1110-2-1417, Hydrol. Eng. Center, Davis, Calif.
46. Vogel, R. M., and I. Wilson (1996), Probability distribution of annual maximum, mean, and minimum streamflows in the United Sates, J. Hydrol. Eng., 1(2), 69-76, doi:10.1061/(ASCE)1084-0699(1996)1:2(69).
47. Vogel, R. M., C. Yaindl, and M. Walter (2011), Nonstationarity: Flood magnification and recurrence reduction factors in the United States, J. Am. Water Resour. Assoc., 47(3), 464-474, doi:10.1111/j.1752-1688.2011.00541.x.
48. Wang, R. C. (2000), Hydropower Engineering in China: Engineering Hydrology [in Chinese], China Electr. Power Press, Beijing.
49. Xiong, L., and S. Guo (1999), A two-parameter monthly water balance model and its application, J. Hydrol., 216, 111-123, doi:10.1016/ S0022-1694(98)00297-2.
50. Xiong, L., and S. Guo (2012), Appraisal of Budyko formula in calculating long-term water balance in humid watersheds of the Southern China, Hydrol. Processes, 26(9), 1370-1378, doi:10.1002/hyp.8273.
51. Yang, D., F. Sun, Z. Liu, Z. Cong, G. Ni, and Z. Lei (2007), Analyzing spatial and temporal variability of annual water-energy balance in nonhumid regions of China using the Budyko hypothesis, Water Resour. Res., 43, W04426, doi:10.1029/2006WR005224.
52. Yu, K.-x., L. Xiong, and L. Gottschalk (2014), Derivation of low flow distribution functions using copulas, J. Hydrol., 508, 273-288, doi: 10.1016/j.jhydrol.2013.09.057.
53. Zhang, L., W. R. Dawes, and G. R. Walker (2001), Response of mean annual evapotranspiration to vegetation changes at catchment scale, Water Resour. Res., 37(3), 701-708, doi:10.1029/2000WR900325.
54. Zhang, L., K. Hickel, W. R. Dawes, F. H. S. Chiew, A. W. Western, and P. R. Briggs (2004), A rational function approach for estimating mean annual evapotranspiration, Water Resour. Res., 40, W02502, doi:10.1029/2003WR002710.
55. Zhang, L., N. Potter, K. Hickel, Y. Zhang, and Q. Shao (2008), Water balance modeling over variable time scales based on the Budyko framework-Model development and testing, J. Hydrol., 360, 117-131, doi:10.1016/j.jhydrol.2008.07.021.