A new approach to simulating stream isotope dynamics using Markov switching autoregressive models

Advances in Water Resources

Volumn 46, Issue , 2012, Pages 20-30

  Birkel, Christian ^a   Paroli, Roberta ^b   Spezia, Luigi ^c   Dunn, Sarah M ^d   Tetzlaff, Doerthe ^a   Soulsby, Chris ^a  

^a UNIVERSITY OF ABERDEEN   (United Kingdom)

^b UNIVERSITÀ CATTOLICA DEL SACRO CUORE   (Italy)

^c BIOMATHEMATICS AND STATISTICS SCOTLAND   (United Kingdom)

^d SCOTTISH CROP RESEARCH INSTITUTE   (United Kingdom)

Author keywords

Bayesian inference; Complex stochastic systems; Markov chains; Non linearity; Stable isotopes; Tracers

Indexed keywords

BAYESIAN APPROACHES; BAYESIAN INFERENCE; CATCHMENT SYSTEM; COVARIATES; FIRST ORDER; HIDDEN STATE; HIGH RATE; HYDROGRAPH SEPARATION; MARKOV CHAIN MONTE CARLO ALGORITHMS; MARKOV-SWITCHING AUTOREGRESSIVE MODELS; MISSING VALUES; NON-LINEARITY; NONSTATIONARY; OXYGEN-18; PROOF OF CONCEPT; SCOTLAND; SMALL CATCHMENT; STABLE ISOTOPES; STATISTICAL CHARACTERISTICS; STREAM WATER; TEMPORAL DYNAMICS; TIME SERIES CHARACTERISTIC; TRANSIT TIME; TRANSPORT MECHANISM; WATER ISOTOPE;

ATMOSPHERIC MOVEMENTS; BAYESIAN NETWORKS; CATCHMENTS; DEUTERIUM; INFERENCE ENGINES; MARKOV PROCESSES; RADIOACTIVE TRACERS; REGRESSION ANALYSIS; TIME SERIES;

DYNAMICS;

BAYESIAN ANALYSIS; CATCHMENT; DEUTERIUM; ISOTOPIC ANALYSIS; ISOTOPIC COMPOSITION; MARKOV CHAIN; REGRESSION ANALYSIS; STABLE ISOTOPE; STREAMWATER; TEMPORAL ANALYSIS; TIME SERIES ANALYSIS; TRACER;

EID: 84864134009     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2012.05.013     Document Type: Article

References (48)

1. Kendall C., McDonnell J.J. Isotope tracers in catchment hydrology 1998, Elsevier, Amsterdam.
2. McDonnell J.J., McGuire K., Aggarwal P., Beven K., Biondi D., Destouni G., Dunn S., James A., Kirchner J., Kraft P., Lyon S., Malowszewski P., Newman B., Pfister L., Rinaldo A., Rodhe A., Sayama T., Seibert T., Soloman K., Soulsby C., Stewart M., Tetzlaff D., Tobin C., Troch P., Weiler M., Western A., Wormann A., Wrede S. How old is the water? Open questions in catchment transit time conceptualisation, modelling and analysis. Hydrol Process 2010, 24:1745-1754.
3. Kirchner J. A double paradox in catchment hydrology and geochemistry. Hydrol Process 2003, 17:871-874.
4. Neal C., Reynolds B., Norris D., Kirchner J.W., Neal M., Rowland P., Wickham H., Harman S., Armstrong L., Sleep D., Lawlor A., Woods C., Williams B., Fry M., Newton G., Wright D. Three decades of water quality measurements from the Upper Severn experimental catchments at Plynlimon, Wales: an openly accessible data resource for research, modelling, environmental management and education. Hydrol Process 2011, 25:3818-3830.
5. McGuire K.J., McDonnell J.J. A review and evaluation of catchment transit time modelling. J Hydrol 2006, 330:543-563.
6. Hrachowitz M., Soulsby C., Tetzlaff D., Speed M. Catchment transit times and landscape controls - does scale matter?. Hydrol Process 2010, 24:117-125.
7. Fenicia F., Wrede S., Kavetski D., Pfister L., Hoffmann L., Savenije H.H.G., McDonnell J.J. Assessing the impact of mixing assumptions on the estimation of streamwater mean residence time. Hydrol Process 2010, 24:1730-1741.
8. Birkel C., Soulsby C., Tetzlaff D., Dunn S.M., Spezia L. High-frequency storm event isotope sampling reveals time-variant transit time distributions and influence of diurnal cycles. Hydrol Process 2012, 26:308-316.
9. Beven K. On the future of distributed modelling in hydrology. Hydrol Process 2000, 14:3183-3184.
10. Sivapalan M., Blöschl G., Zhang L., Vertessy R. Downward approach to hydrological prediction. Hydrol Process 2003, 17:2101-2111.
11. Botter G., Milan E., Bertuzzo E., Zanardo S., Marani M. Rinaldo. Inferences from catchment-scale tracer circulation experiments. J Hydrol 2009, 369:368-380.
12. Botter G., Porporato A., Rodriguez-Iturbe I., Rinaldo A. Nonlinear storage-discharge relations and catchment streamflow regimes. Water Resour Res 2009, 45:W10427.
13. McGuire K.J., Weiler M., McDonnell J.J. Integrating tracer experiments with modeling to assess runoff processes and water transit times. Adv Water Resour 2006, 30:824-837.
14. Hrachowitz M., Soulsby C., Tetzlaff D., Malcolm I.A., Schoups G. Gamma distribution models for transit time estimation in catchments: physical interpretation of parameters and implications for time-variant transit time assessment. Water Resour Res 2010, 46:W10536.
15. Rinaldo A., Beven K.J., Bertuzzo E., Nicotina L., Davies J., Fiori A., Russo D., Botter G. Catchment travel time distributions and water flow in soils. Water Resour Res 2011, 47:W07537.
16. Milly P.C.D., Betancourt J., Falkenmark M., Hirsch R.M., Kundzewicz Z.W., Lettenmaier D.P., Stouffer R.J. Stationarity is dead: whither water management?. Science 2008, 319:573-574.
17. Hamilton J.D. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 1989, 57:357-384.
18. Hamilton J.D. Analysis of time series subject to changes in regime. J Econ 1990, 45:39-70.
19. Hamilton J.D. Estimation, inference and forecasting of time series subject to changes in regime. Handbook of statistics 1993, vol. 11:231-259. North-Holland, Amsterdam.
20. Lu Z.-Q., Berliner L.M. Markov switching time series models with application to a daily runoff series. Water Resour Res 1999, 35:523-534.
21. Gelati E., Madsen H., Rosbjerg D. Markov-switching models for nonstationary runoff conditioned on El Niño information. Water Resour Res 2010, 46:W02517.
22. Ailliot P., Thompson C., Thomson P. Space-time modelling of precipitation by using a hidden Markov model and censored Gaussian distributions. Appl Stat 2009, 58:405-426.
23. Akintuĝ B., Rasmussen P.F. A Markov switching model for annual hydrological time series. Water Resour Res 2005, 41:W09424.
24. Jayawardena A.W., Xu P.C., Li W.K. Rainfall data simulation by hidden Markov model and discrete wavelet transformation. Stoch Env Res Risk Assess 2009, 23:863-877.
25. Spezia L., Futter M.N., Brewer M.J. Periodic multivariate Normal hidden Markov models for the analysis of water quality time series. Environmetrics 2011, 22:304-317.
26. Paroli R., Spezia L. Bayesian inference in non-homogeneous Markov mixture of periodic autoregressions with state-dependent exogenous variables. Comput Stat Data Anal 2008, 52:2311-2330.
27. Kirchner J.W., Feng X., Neal C. Fractal stream chemistry and its implications for contaminant transport in catchments. Nature 2000, 403:524-527.
28. Diebolt F.X., Inoue A. Long memory and regime switching. J Econom 2001, 105:131-159.
29. Birkel C., Dunn S.M., Tetzlaff D., Soulsby C. Assessing the value of high-resolution isotope tracer data in the step-wise development of a lumped conceptual rainfall-runoff model. Hydrol Process 2010, 24:2335-2348.
30. Dunn S.M., Birkel C., Soulsby C., Tetzlaff D. Transit time distributions of a conceptual model: their characteristics and sensitivities. Hydrol Process 2010, 24:1719-1729.
31. Soulsby C., Petry J., Brewer M.J., Dunn S.M., Ott B., Malcolm I.A. Identifying and assessing uncertainty in hydrological pathways: a novel approach to end member mixing in a Scottish agricultural catchment. J Hydrol 2003, 274:109-128.
32. Birkel C., Tetzlaff D., Dunn S.M., Soulsby C. Using lumped conceptual rainfall-runoff models to simulate daily isotope variability with fractionation in a nested mesoscale catchment. Adv Water Resour 2011, 34:383-394.
33. Paroli R., Spezia L. Bayesian variable selection in Markov mixture models. Commun Stat Sim Comput 2008, 37:25-47.
34. Kuo L., Mallick B. Variable selection for regression models. Sankhya B 1998, 60:65-81.
35. Brooks J.R., Barnard H.R., Coulombe R., McDonnell J.J. Ecohydrologic separation of water between trees and streams in a Mediterranean climate. Nature Geosci 2010, 3:100-104.
36. Botter G., Bertuzzo E., Rinaldo A. Catchment residence and travel time distributions: the master equation. Geophys Res Lett 2011, 38:L11403.
37. Richardson S., Green P.J. On Bayesian analysis of mixture with an unknown number of components (with discussion). J Roy Stat Soc B 1997, 59:731-792.
38. Frühwirth-Schnatter S. Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. J Am Stat Assoc 2001, 96:194-209.
39. Kass R.E., Raftery A.E. Bayes factors. J Am Stat Assoc 1995, 90:773-795.
40. Chib S. Marginal likelihood from the Gibbs output. J Am Stat Assoc 1995, 90:1313-1321.
41. Chib S., Jeliazkov I. Marginal likelihoods from the metropolis-hastings output. J Am Stat Assoc 2001, 96:270-281.
42. Spezia L., Paroli R., Dellaportas P. Periodic Markov switching autoregressive models for Bayesian analysis and forecasting of air pollution. Stat Modell 2004, 4:19-38.
43. Schaefli B., Harman C.J., Sivapalan M., Schymanski S.J. HESS opinions: hydrologic predictions in a changing environment: behavioral modeling. Hydrol Earth Syst Sci 2011, 15:635-646.
44. Shaw S.B., Harpold A.A., Taylor J.C., Walter T.M. Investigating a high resolution, stream chloride time series from the biscuit brook catchment, Catskills. NY J Hydrol 2008, 348:245-256.
45. Klemes V. The hurst phenomenon - a puzzle?. Water Resour Res 1974, 10:675-688.
46. Lyon S.W., Desilets S.L.E., Troch P.A. A tale of two isotopes: differences in hydrograph separation for a runoff event when using dD versus d18O. Hydrol Process 2009, 23:2095-2101.
47. Kirchner J.W., Tetzlaff D., Soulsby C. Comparing chloride and water isotopes as hydrological tracers in two Scottish catchments. Hydrol Process 2010, 24:1631-1645.
48. Chib S. Calculating posterior distributions and modal estimates in Markov mixture models. J Econ 1996, 75:79-97.