The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM(ABC)

Water Resources Research

Volumn 51, Issue 11, 2015, Pages 9207-9231

  Sadegh, Mojtaba ^a   Vrugt, Jasper A ^a,b   Xu, Chonggang ^c   Volpi, Elena ^d  

^a University of California at Irvine   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d ROMA TRE UNIVERSITY   (Italy)

Author keywords

approximate Bayesian computation; Nonstationarity; process based model evaluation

Indexed keywords

BAYESIAN NETWORKS; CATCHMENTS; FLOW OF WATER; LAND USE; MULTIVARIANT ANALYSIS; NONLINEAR PROGRAMMING;

APPROXIMATE BAYESIAN; HYDROCLIMATIC CONDITIONS; HYDROLOGIC MODELING; NON-STATIONARITIES; NONLINEAR OPTIMIZATION METHODS; PROCESS-BASED MODELING; RESEARCH COMMUNITIES; STATIONARY CONDITIONS;

WATERSHEDS;

ALGORITHM; BAYESIAN ANALYSIS; CATCHMENT; HYDROLOGICAL MODELING; HYPOTHESIS TESTING; LAND USE CHANGE; MULTIVARIATE ANALYSIS; OPTIMIZATION; PARADIGM SHIFT; TEMPORAL VARIATION; URBANIZATION; WATER FLOW; WATERSHED;

EID: 84946861083     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2014WR016805     Document Type: Article

References (112)

1. Alexander, L. V., et al., (2006), Global observed changes in daily climate extremes of temperature and precipitation, J. Geophys. Res., 111, D05109, doi: 10.1029/2005JD006290.
2. Anghileri, D., F. Pianosi, and, R. Soncini-Sessa, (2014), Trend detection in seasonal data: From hydrology to water resources, J. Hydrol., 511, 171-179.
3. Bassiouni, M., and, D. S. Oki, (2013), Trends and shifts in streamflow in Hawaii, 1913-2008, Hydrol. Processes, 27 (10), 1484-1500.
4. Beaumont, M. A., W. Zhang, and, D. J. Balding, (2002), Approximate Bayesian computation in population genetics, Genetics, 162 (4), 2025-2035.
5. Birsan, M. V., P. Molnar, P. Burlando, M. Pfaundler, (2005), Streamflow trends in Switzerland, J. Hydrol., 314, 312-329.
6. Boyle, D., (2001), Multicriteria calibration of hydrological models, PhD dissertation, Univ. of Arizona, Tucson.
7. Buishand, T. A., (1982), Some methods for testing the homogeneity of rainfall records, J. Hydrol., 58, 11-27.
8. Burn, D. H., and, M. A. Hag Elnur, (2002), Detection of hydrologic trends and variability, J. Hydrol., 255, 107-122.
9. Burnash, R. J., R. L. Ferral, and, R. A. McGuire, (1973), A Generalized Streamflow Simulation System: Conceptual Modeling for Digital Computers, Joint Fed.-State River Forecast Cent., Sacramento, Calif.
10. Chebana, F., T. B. M. J. Ouarda, and, T. C. Duong, (2013), Testing for multivariate trends in hydrologic frequency analysis, J. Hydrol., 486, 519-530.
11. Clarke, R. T., (2002), Estimating trends in data from the Weibull and a generalized extreme value distribution, Water Resour. Res., 38 (6), doi: 10.1029/2001WR000575.
12. Clarke, R. T., (2007), Hydrological prediction in a non-stationary world, Hydrol. Earth Syst. Sci., 11, 408-414, doi: 10.5194/hess-11-408-2007.
13. Clausen B., and, B. J. F. Biggs, (2000), Flow variables for ecological studies in temperate streams: Grouping based on covariance, J. Hydrol., 237 (3-4), 184-197.
14. Cong, Z., D. Yang, B. Gao, H. Yang, and, H. Hu, (2009), Hydrological trend analysis in the Yellow River basin using a distributed hydrological model, Water Resour. Res., 45, W00A13, doi: 10.1029/2008WR006852.
15. Cunderlik, J. M., and, D. H. Burn, (2003), Non-stationary pooled flood frequency analysis, J. Hydrol., 276, 210-223.
16. Cunderlik, J. M., and, T. B. M. J. Ouarda, (2006), Regional flood-duration-frequency modeling in a changing environment, J. Hydrol., 318, 276-291.
17. Cunnane, C., (1988), Methods and merits of regional flood frequency analysis, J. Hydrol., 100 (1-3), 269-290.
18. Del Moral, P., A. Doucet, and, A. Jasra, (2012), An adaptive sequential Monte Carlo method for approximate Bayesian computation, Stat. Comp., 22 (5), 1009-1020.
19. Dettinger, M., (2011), Climate change, atmospheric rivers, and floods in California-A multimodel analysis of storm frequency and magnitude changes, J. Am. Water Resour. Assoc., 47, 514-523.
20. Diggle, P. J., and, R. J. Gratton, (1984), Monte Carlo methods of inference for implicit statistical models, J. R. Stat. Soc., Ser. B, 46, 193-227.
21. Douglas, E. M., R. M. Vogel, and, C. N. Kroll, (2000), Trends in floods and low flows in the United States: Impact of spatial correlation, J. Hydrol., 240 (1-2), 90-105.
22. Eckhardt, K., (2005), How to construct recursive digital filters for baseflow separation, Hydrol. Processes, 19, 507-515.
23. Edwards, A. W. F., (1992), Likelihood, The Johns Hopkins Univ. Press, Baltimore, Md.
24. El-Adlouni, S., T. B. M. J. Ouarda, X. Zhang, R. Roy, and, B. Bobée, (2007), Generalized maximum likelihood estimators for the nonstationary generalized extreme value model, Water Resour. Res., 43, W03410, doi: 10.1029/2005WR004545.
25. Euser, T., H. C. Winsemius, M. Hrachowitz, F. Fenicia, S. Uhlenbrook, and, H. H. G. Savenije, (2013), A framework to assess the realism of model structures using hydrological signatures, Hydrol. Earth Syst. Sci., 17, 1893-1912, doi: 10.5194/hess-17-1893-2013.
26. Fu, G., S. Chen, C. Liu, and, D. Shepard, (2004), Hydro-climatic trends of the Yellow River basin for the last 50 years, Clim. Change, 65 (1-2), 149-178.
27. Gelman, A., and, D. B. Rubin, (1992), Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457-472.
28. Graf, W. L., (1977), Network characteristics in suburbanizing streams, Water Resour. Res., 13 (2), 459-463.
29. Groisman, P. Y., R. W. Knight, and, T. R. Karl, (2001), Heavy precipitation and high streamflow in the contiguous United States: Trends in the twentieth century, Bull. Am. Meteorol. Soc., 82, 219-246.
30. Groisman, P. Y., R. W. Knight, T. R. Karl, D. R. Easterling, B. Sun, and, J. H. Lawrimore, (2004), Contemporary changes of the hydrological cycle over the contiguous United States: Trends derived from in situ observations, J. Hydrometeorol., 5, 64-85.
31. Gupta, H. V., T. Wagener, and, Y. Liu, (2008), Reconciling theory with observations: Elements of a diagnostic approach to model evaluation, Hydrol. Processes, 22 (18), 3802-3813.
32. Hodgkins, G. A., and, R. W. Dudley, (2006), Changes in the timing of Winter-Spring streamflows in Eastern North America, 1913-2002, Geophys. Res. Lett., 33, L06402, doi: 10.1029/2005GL025593.
33. Hurst, H. E., (1951), Long term storage capacities of reservoirs, Trans. Am. Soc. Civ. Eng., 116, 776-808.
34. Ishak, E. H., A. Rahman, S. Westra, A. Sharma, and, G. Kuczera, (2013), Evaluating the non-stationarity of Australian annual maximum flood, J. Hydrol., 494, 134-145.
35. Jain, S., and, U. Lall, (2001), Floods in a changing climate: Does the past represent the future?, Water Resour. Res., 37 (12), 3193-3205, doi: 10.1029/2001WR000495.
36. Joshi, M. K., and, A. C. Pandey, (2011), Trend and spectral analysis of rainfall over India during 1901-2000, J. Geophys. Res., 116, D06104, doi: 10.1029/2010JD014966.
37. Karl, T. R., and, R. W. Knight, (1998), Secular trends of precipitation amount, frequency, and intensity in the United States, Bull. Am. Meteorol. Soc., 79 (2), 231-241.
38. Karthikeyan, L., and, D. Nagesh Kumar, (2013), Predictability of nonstationary time series using wavelet and EMD based ARMA models, J. Hydrol., 502, 103-119.
39. Khaliq, M. N., T. B. M. J. Ouarda, P. Gachon, L. Sushama, and, A. St-Hilaire, (2009), Identification of hydrological trends in the presence of serial and cross correlations: A review of selected methods and their application to annual flow regimes of Canadian rivers, J. Hydrol., 368, 117-130.
40. Koutsoyiannis, D., (2006), Nonstationarity versus scaling in hydrology, J. Hydrol., 324, 239-254.
41. Koutsoyiannis, D., (2011), Hurst-Kolmogorov dynamics and uncertainty, J. Am. Water Resour. Assoc., 47 (3), 481-495.
42. Koutsoyiannis, D., (2013), Hydrology and change, Hydrol. Sci. J., 58 (6), 1177-1197, doi: 10.1080/02626667.2013.804626.
43. Koutsoyiannis, D., and, A. Montanari, (2014), Negligent killing of scientific concepts: The stationarity case, Hydrol. Sci. J., 60 (7-8), 1174-1183, doi: 10.1080/02626667.2014.959959.
44. Kundzewicz, Z. W., (2011), Nonstationarity in water resources-Central European perspective, J. Am. Water Resour. Assoc., 47, 550-562.
45. Kundzewicz, Z. W., and, A. J. Robson, (2004), Change detection in hydrological records: A review of the methodology, Hydrol. Sci., 49, 7-19.
46. Kundzewicz, Z. W., D. Graczyk, T. Maurer, I. Pińskwar, M. Radziejewski, C. Svensson, and, M. Szwed, (2005), Trend detection in river flow series: 1. Annual maximum flow, Hydrol. Sci. J., 50 (5), 797-810, doi: 10.1623/hysj.2005.50.5.797.
47. (ZS) and high-performance computing, Water Resour. Res., 48, W01526, doi: 10.1029/2011WR010608.
48. Leclerc, M., and, T. B. M. J. Ouarda, (2007), Non-stationary regional flood frequency analysis at ungauged sites, J. Hydrol., 343, 254-265.
49. Lettenmaier, D. P., E. F. Wood, and, J. R. Wallis, (1994), Hydroclimatological trends in the continental United States, 1948-1988, J. Clim., 7, 586-607.
50. Lima, C. H. R., and, U. Lall, (2010), Spatial scaling in a changing climate: A hierarchical Bayesian model for non-stationary multi-site annual maximum and monthly streamflow, J. Hydrol., 383 (3-4), 307-318.
51. Lins, H. F., (1985), Streamflow variability in the United States: 1931-78, J. Clim. Appl. Meteorol., 24, 463-471.
52. Lins, H. F., and, T. A. Cohn, (2011), Stationarity: Wanted dead or alive?, J. Am. Water Resour. Assoc., 47 (3), 475-480.
53. Lins, H. F., and, J. R. Slack, (1999), Streamflow trends in the United States, Geophys. Res. Lett., 26 (2), 227-230.
54. Lins, H. F., and, J. R. Slack, (2005), Seasonal and regional characteristics of U.S. streamflow trends in the United States from 1940-1999, Phys. Geogr., 26, 489-501.
55. Marjoram, P., J. Molitor, V. Plagnol, and, S. Tavaré, (2003), Markov chain Monte Carlo without likelihoods, Proc. Natl. Acad. Sci. U. S. A., 100 (26), 15,324-15,328.
56. McCabe, G. J., and, D. M. Wolock, (2002), A step increase in streamflow in the coterminous United States, Geophys. Res. Lett., 29 (24), 2185, doi: 10.1029/2002GL015999.
57. Milly, P. C. D., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. Kundzewicz, D. P. Lettenmaier, and, R. J. Stouffer, (2008), Stationarity is dead: Whiter water management?, Science, 319, 573-574.
58. Morin, E., K. P. Georgakakos, U. Shamir, R. Garti, and, Y. Enzel, (2002), Objective, observations-based, automatic estimation of the catchment response timescale, Water Resour. Res., 38 (10), 1212, doi: 10.1029/2001WR000808.
59. Mroczkowski, M., G. P. Raper, and, G. Kuczera, (1997), The quest for more powerful validation of conceptual catchment models, Water Resour. Res., 33 (10), 2325-2335.
60. Nasri, B., S. El-Adlouni, and, T. B. M. J. Ouarda, (2013), Bayesian estimation for GEV-B-Spline model, Open J. Stat., 3 (2), 118-128.
61. Ni, C. F., C. P. Lin, S. G. Li, and, C. J. Liu, (2011), Efficient approximate spectral method to delinate stochastic well capture zones in nonstationary groundwater flow systems, J. Hydrol., 407 (1-4), 184-195.
62. North, M., (1980), Time-dependent stochastic model of floods, J. Hydraul. Div., 106 (5), 649-665.
63. Novotny, E. V., and, H. G. Stefan, (2007), Stream flow in Minnesota: Indicator of climate change, J. Hydrol., 334, 319-333.
64. Olden, J. D., and, N. L. Poff, (2003), Redundancy and the choice of hydrologic indices for characterizing streamflow regimes, River Res. Appl., 19, 101-121.
65. Ouarda, T. B. M. J., and, S. El-Adlouni, (2011), Bayesian nonstationary frequency analysis of hydrological variables, J. Am. Water Resour. Assoc., 47 (3), 496-505.
66. Parey, S., F. Malek, C. Laurent, and, D. Dacunha-Castelle, (2007), Trends and climate evolution: Statistical approach for very high temperatures in France, Clim. Change, 81 (3-4), 331-352.
67. Petrow, T., and, B. Merz, (2009), Trends in flood magnitude, frequency and seasonality in Germany in the period 1951-2002, J. Hydrol., 371, 129-141.
68. Pitman, W. V., (1978), Trends in streamflow due to upstream land-use changes, J. Hydrol., 39, 227-237.
69. Potter, K. W., (1991), Hydrological impacts of changing land management practices in a moderate-sized agricultural catchment, Water Resour. Res., 27 (5), 845-855.
70. Price, K. V., R. M. Storn, and, J. A. Lampinen, (2005), Differential Evolution: A Practical Approach to Global Optimization, Springer, Berlin.
71. Pritchard, J. K., M. T. Seielstad, A. Perez-Lezaun, and, M. T. Feldman, (1999), Population growth of human Y chromosomes: A study of Y chromosome microsatellites, Mol. Biol. Evol., 16 (12), 1791-1798.
72. Ramachandra Rao, A., and, G. H. Yu, (1986), Detection of nonstationarity in hydrologic time series, Manage. Sci., 32 (9), 1206-1217.
73. Renard, B., M. Lang, and, P. Bois, (2006), Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: Case study with peak-over-threshold data, Stochastic Environ. Res. Risk Assess., 21, 97-112.
74. Rougé, C., Y. Gea, and, X. Cai, (2013), Detecting gradual and abrupt changes in hydrological records, Adv. Water Res., 53, 33-44.
75. Sadegh, M., and, J. A. Vrugt, (2013), Bridging the gap between GLUE and formal statistical approaches: Approximate Bayesian computation, Hydrol. Earth Syst. Sci., 17, 4831-4850, doi: 10.5194/hess-17-4831-2013.
76. (ABC), Water Resour. Res., 50, 6767-6787, doi: 10.1002/2014WR015386.
77. Salas, J. D., and, J. Obeysekera, (2014), Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events, J. Hydrol. Eng., 19 (3), 554-568.
78. Savenije, H. H. G., (1996), The runoff coefficient as the key to moisture recycling, J. Hydrol., 176, 219-225.
79. Schaake, J., S. Cong, and, Q. Duan, (2006), U.S. MOPEX Data Set, IAHS Publ. Ser., Lawrence Livermore Natl. Lab., Livermore, Calif. [Available at http://goo.gl/wthGvS.]
80. Scharnagl, B., J. A. Vrugt, H. Vereecken, and, M. Herbst, (2011), Bayesian inverse modeling of soil water dynamics at the field scale: Using prior information about the soil hydraulic properties, Hydrol. Earth Syst. Sci., 15, 3043-3059, doi: 10.5194/hess-15-3043-2011.
81. Schoups, G., and, J. A. Vrugt, (2010), A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-Gaussian errors, Water Resour. Res., 46, W10531, doi: 10.1029/2009WR008933.
82. Searcy, J. K., (1959), Flow-duration curves, U.S. Geol. Surv. Water Supply Pap., 1542-A, 17-21.
83. Shamir, E., B. Imam, E. Morin, H. V. Gupta, and, S. Sorooshian, (2005), The role of hydrograph indices in parameter estimation of rainfall-runoff models, Hydrol. Processes, 19, 2187-2207.
84. Sisson, S. A., Y. Fan, and, M. M. Tanaka, (2007), Sequential Monte Carlo without likelihoods, Proc. Natl. Acad. Sci. U. S. A., 104 (6), 1760-1765.
85. Smith, J. A., M. L. Baeck, J. E. Morrison, P. Sturdevant-Rees, D. F. Turner-Gillespie, and, P. D. Bates, (2002), The regional hydrology of extreme floods in an urbanizing drainage, J. Hydrometeorol., 3 (3), 267-282.
86. Stedinger, J. R., and, V. W. Griffis, (2011), Getting from here to where? Flood frequency analysis and climate, J. Am. Water Resour. Assoc., 47, 506-513.
87. Storn, R., and, K. Price, (1997), Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., 11, 341-359.
88. Strupczewski, W. G., V. P. Singh, and, H. T. Mitosek, (2001), Non-stationary approach to at-site flood frequency modelling. III. Flood analysis of Polish rivers, J. Hydrol., 248 (1-4), 152-167.
89. Svensson, C., W. Z. Kundzewicz, and, T. Maurer, (2005), Trend detection in river flow series: 2. Flood and low-flow index series, Hydrol. Sci. J., 50 (5), 811-824.
90. Thirel, G., et al., (2015), Hydrology under change: An evaluation protocol to investigate how hydrological models deal with changing catchments, Hydrol. Sci. J., 60, 1184-1199, doi: 10.1080/02626667.2014.967248.
91. Turner, B. M., and, T. van Zandt, (2012), A tutorial on approximate Bayesian computation, J. Math. Psychol., 56, 69-85.
92. Vaze, J., D. A. Post, F. H. S. Chiew, J.-M. Perraud, N. R. Viney, and, J. Teng, (2010), Climate non-stationarity-Validity of calibrated rainfall-runoff models for use in climate change studies, J. Hydrol., 394, 447-457.
93. Villarini, G., and, J. A. Smith, (2010), Flood peak distributions for the eastern United States, Water Resour. Res., 46, W06504, doi: 10.1029/2009WR008395.
94. Villarini, G., F. Serinaldi, J. A. Smith, and, W. F. Krajewski, (2009), On the stationarity of annual flood peaks in the continental United States during the 20th century, Water Resour. Res., 45, W08417, doi: 10.1029/2008WR007645.
95. 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.
96. Vrugt, J. A., (2015), Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation, Environ. Model. Software, doi: 10.13140/RG.2.1.4692.6569.
97. Vrugt, J. A., and, M. Sadegh, (2013), Toward diagnostic model calibration and evaluation: Approximate Bayesian computation, Water Resour. Res., 49, 4335-4345, doi: 10.1002/wrcr.20354.
98. Vrugt, J. A., C. G. H. Diks, W. Bouten, H. V. Gupta, and, J. M. Verstraten, (2005), Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation, Water Resour. Res., 41, W01017, doi: 10.1029/2004WR003059.
99. Vrugt, J. A., C. J. F. ter Braak, M. P. Clark, J. M. Hyman, and, B. A. Robinson, (2008), Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation, Water Resour. Res., 44, W00B09, doi: 10.1029/2007WR006720.
100. Vrugt, J. A., C. J. F. ter Braak, C. G. H. Diks, D. Higdon, B. A. Robinson, and, J. M. Hyman, (2009), Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling, Int. J. Nonlinear Sci. Numer. Simul., 10 (3), 273-290.
101. Waage, M. D., and, L. Kaatz, (2011), Nonstationary water planning: An overview of several promising planning methods, J. Am. Water Resour. Assoc., 47, 535-540.
102. Westerberg, I., J.-L. Guerrero, J. Seibert, K. J. Beven, and, S. Halldin, (2011), Stage-discharge uncertainty derived with a non-stationary rating curve in the Choluteca River, Honduras. Hydrol. Processes, 25, 603-613, doi: 10.1002/hyp.7848.
103. Westmacott, J. R., and, D. H. Burn, (1997), Climate change effects on the hydrologic regime within the Churchill-Nelson River basin, J. Hydrol., 202 (1-4), 263-279.
104. Westra, S., and, S. A. Sisson, (2011), Detection of non-stationarity in precipitation extremes using a max-stable process model, J. Hydrol., 406 (1-2), 119-128.
105. Westra, S., L. V. Alexander, and, F. W. Zwiers, (2013), Global increasing trends in annual maximum daily precipitation, J. Clim., 26, 3904-3918.
106. Westra, S., M. Thyer, M. Leonard, D. Kavetski, and, M. Lambert, (2014), A strategy for diagnosing and interpreting hydrologic non-stationarity, Water Resour. Res. 50, 5090-5113, doi: 10.1002/2013WR014719.
107. Xu, C.-Y., L. Gong, T. Jiang, D. Chen, and, V. P. Singh, (2006), Analysis of spatial distribution and temporal trend of reference evapotranspiration and pan evaporation in Changjiang (Yangtze River) catchment, J. Hydrol., 327 (1-2), 81-93.
108. Yadav, M., T. Wagener, and, H. Gupta, (2007), Regionalization of constraints on expected watershed response behavior for improved predictions in ungauged basins, Adv. Water Resour., 30, 1756-1774.
109. Yue, S., P. Pilon, and, G. Cavadias, (2002), Power of the Mann-Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series, J. Hydrol., 264 (1-4), 262-263.
110. Zhang, Q., C.-Y. Xu, S. Becker, Z. X. Zhang, Y. D. Chen, and, M. Coulibaly, (2009), Trends and abrupt changes of precipitation maxima in the Pearl River basin, China, Atmos. Sci. Lett., 10, 132-144, doi: 10.1002/asl.221.
111. Zhang, X., K. D. Harvey, W. D. Hogg, and, T. R. Yuzyk, (2001), Trends in Canadian streamflow, Water Resour. Res., 37 (4), 987-998.
112. Zhang, Y. K., and, K. E. Schilling, (2006), Increasing streamflow and baseflow in Mississippi River since the 1940s: Effect of land use change, J. Hydrol., 324, 412-422.