بررسی عدم قطعیت ناشی از پیچیدگی مدل‌های ستون تجربی انتقال آلاینده از دیدگاه محلی و منطقه‌ای

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری هیدروژئولوژی/گروه علوم زمین دانشگاه تبریز. تبریز. ایران

2 دکتری هیدروژئولوژی/ استاد /گروه علوم زمین دانشگاه تبریز. تبریز. ایران

چکیده

شناسایی پیچیدگی در مدل‌های جایگزین ستون تجربی انتقال آلاینده منجر به انتخاب مدل بهینه و بهترین برآورد از پارامتر می‌گردد و از عدم قطعیت ناشی از پیچیدگی و نتایج غیر صحیح جلوگیری می‌نماید. در این مطالعه جهت بررسی عدم قطعیت ناشی از پیچیدگی در مدل‌های ستون تجربی چهار مدل مفهومی مختلف با درجه های پیچیدگی متفاوت شامل: مدل‌های تعادلی کانوکشن-دیسپرژن، CDE1 (ساده‌ترین مدل با یک پارامتر) و CDE2 ، مدل‌های غیر تعادلی متحرک- غیر متحرک، MIM1 و MIM2(پیچیده‌ترین مدل با چهار پارامتر)، با دو وضعیت سرعت جریان بالا q36.7 و سرعت جریان پایین q2.71 از منابع استفاده گردیده است. آنالیز مدل‌های جایگزین ستون تجربی از طریق چهار روش: 1- امتیازدهی به مدل ها بر اساس RMSE . 2- ارزیابی احتمال مدل‌های جایگزین از طریق روش معیارهای انتخاب مدل( AIC، AICC، BIC و KIC) 3- ارزیابی احتمالات مدل از طریق میانگین حسابی یا AME با روش مونت کارلو و 4- روش برآورد احتمالات مدل از طریق میانگین هارمونیک یا HME از طریق زنجیره مارکوف مونت کارلو ( MCMC) دارای یک توسعه تدریجی از دیدگاه محلی به سمت دیدگاه منطقه‌ای می‌باشد. نتایج نهایی در ارزیابی مدل‌ها نشان می‌دهد که امتیاز بندی مدل‌ها در روش‌های محلی با روش‌های منطقه‌ای متفاوت هستند. در یک نتیجه گیری کلی پیچیدگی در وضعیت سرعت جریان بالا تا حد مدل MIM1 و در وضعیت سرعت جریان پایین تا حد مدل CDE2 کافی می‌باشد و پیچیده کردن مدل‌های انتقال بیشتر از این حد منجر به افزایش عدم قطعیت مدل می‌گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Exploring Uncertainty Caused by Model Complexity in Column Experiments from Local and Global Perspectives

نویسندگان [English]

  • S Samani 1
  • A Asghari Moghaddam 2
1 Ph.D Student of Hydrogeology, Geology Department, University of Tabriz , Tabriz, Iran
2 Ph.D in Hydrogeology, Professor, Geology Department, University of Tabriz, Tabriz, Iran
چکیده [English]

Considering the complexity of contaminant transport models in column experiments, can aid selection of an optimal model and best estimation of model parameters, avoid over parameterization, model uncertainty and incorrect conclusions. We consider tow experiment with high flow velocity (q36.7) and low flow velocity (q2.71) with four models of different levels of complexity, including the equilibrium and non-equilibrium convection dispersion models. Consists of the convection-dispersion models CDE1 (The simplest model with one parameter) and CDE2, and mobile-immobile models MIM1 and MIM2 (the most complex model with four parameters). Through analysis of column experiments, we can view the four approaches: 1- ranking the models based on the RMSE, 2- Evaluate model probability through model selection criteria (AIC, AICc, BIC, and KIC statistics). 3- Evaluate model probability using the arithmetic mean estimated using the Monte Carlo method, and 4- Evaluate model probability using the harmonic mean estimated using the Markov chain Monte Carlo method as a gradual expansion from the local to the global scale of model parameters. The final result is showing that, evaluation of model probability change from local to global scale of model parameters. In a general conclusion, degree of complexity for high flow case to the extent MIM1 and for low flow case to the CDE2 model is enough to avoid uncertainty from over parameterization.

کلیدواژه‌ها [English]

  • 'Model complexity'
  • 'Model uncertainty'
  • 'Column experiment'
  • 'Contaminant transport model'
  • 'Local and global Perspectives'
Akaike H (1974) A new look at the statistical model identification. IEEE transactions on automatic control 19(6):716-723
Anamosa PR, Nkedi-Kizza P, Blue WG,  Sartain JB (1990) Water movement through an aggregated, gravelly oxisol from Cameroon. Geoderma 46(1):263-281
Anderson MP, Woessner WW (1992) Applied groundwater modeling—simulation of flow and advective transport. Academic Press. Inc, New York, 381 p
Bear J, Verruijt A (1987) Modeling groundwater flow and pollution. Springer Science & Business Media. Berlin, 414p
Comegna V, Coppola A, Sommella A (2001) Effectiveness of equilibrium and physical non-equilibrium approaches for interpreting solute transport through undisturbed soil columns. Journal of contaminant hydrology 50(1):121-138
Engelhardt I, Aguinaga JG, Mikat H, Schüth C, Liedl R )2014( Complexity vs. simplicity: groundwater model ranking using information criteria. Groundwater 52(4):573-583
 Finsterle S, Zhang Y (2011) Error handling strategies in multiphase inverse modeling. Computers & Geosciences 37(6):724-730
Foglia L, Mehl SW, Hill MC, Perona P, Burlando P (2007). Testing alternative ground water models using cross‐validation and other methods. Groundwater 45(5):627-641
Foglia L, Mehl SW, Hill MC, Burlando P (2013) Evaluating model structure adequacy: The case of the Maggia Valley groundwater system, southern Switzerland. Water Resources Research 49(1):260-282
 Giacopetti M, Crestaz E, Materazzi M, Pambianchi G, Posavec K (2016) A multi-model approach using statistical index and information criteria to evaluate the adequacy of the model geometry in a fissured carbonate aquifer (Italy). Water 8(7):271
Good PI, Good P (2013) Resampling methods: A practical guide to data analysis. Springer Science & Business Media. Berlin, 265p
Haitjema H )2011( Model complexity: A cost-benefit issue. Geological Society of America 43(5)
Hill MC (2006) The practical use of simplicity in developing ground water models. Groundwater 44(6):775-781
Hoeting J, Madigan D, Raftery A, Volinsky C (1999)  Bayesian model averaging: A tutorial. Statistical Science 14(4):382–401
Hu Q, Brusseau ML (1995) Effect of solute size on transport in structured porous media. Water Resources Research 31(7):1637-1646
Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76(2):297-307
Kashyap RL (1982) Optimal choice of AR and MA parts in autoregressive moving average models. IEEE Transactions on Pattern Analysis and Machine Intelligence (2):99-104
Kass RE, Raftery AE (1995) Bayes factors. Journal of the American statistical association 90 (430):773-795
Liu P, Elshall AS, Ye M, Beerli P, Zeng X, Lu D, Tao Y (2016) Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods. Water Resources Research 52(2):734-758
Lu D, Ye M, Meyer PD, Curtis GP, Shi X, Niu XF, Yabusaki SB (2013) Effects of error covariance structure on estimation of model averaging weights and predictive performance. Water Resources Research 49(9):6029-6047
Lukjan A, Swasdi S, Chalermyanont T (2016) Importance of alternative conceptual model for sustainable groundwater management of the Hat Yai Basin, Thailand. Procedia Engineering 154:308–316
Nettasana T) 2012( Conceptual model uncertainty in the management of the Chi River Basin, Thailand. Thesis, University of Waterloo
 Neuman SP (2003) Maximum likelihood Bayesian averaging of uncertain model predictions: Stochastic Environmental Research and Risk Assessment 17(5):291-305
Newman SP, Wierenga PJ (2003) Comprehensive strategy of hydrogeologic modeling and uncertainty analysis for nuclear facilities and sites. Project, University of Arizona
Padilla IY, Yeh T, Conklin MH (2000) The effect of water content on solute transport in unsaturated porous media. Water Resources Research 35 (11):3303–3313
Parker JC, Van Genuchten MT (1984) Determining transport parameters from laboratory and field tracer experiments. Virginia Agricultural Experiment Station  84(3)
Riva M, Panzeri M, Guadagnini A, Neuman SP (2011) Role of model selection criteria in geostatistical inverse estimation of statistical data‐and model‐parameters. Water Resources Research 47(7)
Rojas R, Feyen L, Dassargues A (2008) Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resources Research 44(12)
Schwarz G (1978) Estimating the dimension of a model. The annals of statistics 6(2):461-464
Seber GAF, Wild C (2003) Nonlinear Regression. John Wiley. New York, 768 p
Simmons CT, Hunt RJ (2012) Updating the debate on model complexity. GSA Today 22(8):28-29
Singh A, Mishra S, Ruskauff G (2010) Model averaging techniques for quantifying conceptual model uncertainty. Groundwater 48(5):701-715
Tang G, Mayes MA, Parker JC, Yin XL, Watson DB, Jardine PM (2009) Improving parameter estimation for column experiments by multi-model evaluation and comparison. Journal of hydrology 376(3):567-578
Tang G, Mayes MA, Parker JC, Jardine PM (2010) CXTFIT/Excel–a modular adaptable code for parameter estimation, sensitivity analysis and uncertainty analysis for laboratory or field tracer experiments. Computers & Geosciences 36(9):1200-1209
Toride N, Leij FJ, Van Genuchten MT (1995) The CXTFIT code for estimating transport parameters from laboratory or filed tracer experiments. US Salinity Laboratory, 132p
Tsai F, Li X (2010) Reply to comment by Ming Ye et al. on “Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window”. Water Resources Research 46(2)
Van Genuchten MT, Wierenga PJ (1976) Mass transfer studies in sorbing porous media I. Analytical solutions. Soil Science Society of America Journal 40(4):473-480
Ye M, Neuman SP, Meyer PD (2004) Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff. Water Resources Research 40(5)
Ye M, Neuman SP, Meyer PD, Pohlmann K (2005) Sensitivity analysis and assessment of prior model probabilities in MLBMA with application to unsaturated fractured tuff. Water Resources Research 41(12)
Ye M, Meyer PD, Neuman SP (2008a) On model selection criteria in multimodel analysis. Water Resources Research 44(3)
Ye M, Pohlmann KF, Chapman JB (2008b) Expert elicitation of recharge model probabilities for the Death Valley regional flow system. Journal of Hydrology 354(1):102-115
Ye M, Pohlmann KF, Chapman JB, Pohll GM, Reeves DM (2010) A model‐averaging method for assessing groundwater conceptual model uncertainty. Groundwater 48(5):716-728
Zhang Y, Yang Y (2015) Cross-validation for selecting a model selection procedure. Journal of Econometrics 187(1):95-112
Zhang Y, Yang G, Li S (2014) Significance of conceptual model uncertainty in simulating carbon sequestration in a deep inclined saline aquifer. Journal of Hazardous, Toxic, and Radioactive Waste 19(3)