بررسی عدم قطعیت پارامترهای خاک بر عدم قطعیت پروفیل رطوبتی با استفاده از نظریه‌ی مجموعه‌های فازی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری/ آبیاری و زهکشی . دانشگاه فردوسی مشهد

2 استاد/ گروه مهندسی آب .دانشگاه فردوسی مشهد

چکیده

عدم قطعیت ابزاری برای سنجش اعتماد پذیری سیستم یا پارامترهای آن می‌باشد. در بررسی حرکت آب در خاک غیر اشباع پارامترهای زیادی موثر هستند، که اندازه‌گیری یا برآورد آن‌ها دشوار بوده و به نوعی دارای عدم قطعیت می‌باشند. در این پژوهش، بر اساس نظریه‌ی مجموعه‌های فازی، رویکردی جایگزین برای بیان نادقیقی پارامترهای مدل و پیش بینی عدم قطعیت در شبیه‌سازی مدل به کار گرفته شد. ابتدا معادله ریچاردز به عنوان یک مدل قطعی برای حرکت آب در خاک به صورت عددی حل گردید. برای به دست آوردن عدم قطعیت در شبیه سازی این مدل، متغیرهای ورودی (θs، θr ، Ks ، α و n) به عنوان توابع فازی معرفی شدند. پس از ساختن توابع فازی مناسب برای هر یک از ورودی‌ها، برای هر برش β مشخص مقادیر مرزی برای این پارامترها به دست آمد، با استفاده از این مقادیر و با درنظر گرفتن قیدهای خاص، مقادیر بیشینه و کمینه رطوبت در زمان و مکان مشخص با استفاده از حل عددی معادله ریچاردز به دست آمد. نتایج نشان داد که عدم قطعیت در شبیه سازی پروفیل رطوبتی خاک در فاز اشباع کمترین و در فاز پیشروی بیش‌ترین مقدار را به خود اختصاص می‌دهد که علت این امر بیش‌ترین اثر عدم قطعیت ذاتی پارامترهای ورودی و نتیجه این عدم قطعیت در پروفیل رطوبتی در فاز پیشروی است. شکل توابع فازی به دست آمده برای رطوبت خاک در زمان مشخص، در عمق‌های مختلف خاک متفاوت بود که متاثر از نقش پارامترهای اولیه در هر زمان و مکان خاص در نتایج خروجی رطوبت می‌باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Uncertainty analysis of soil parameters in soil moisture profile uncertainty using fuzzy set theory

نویسندگان [English]

  • M. Khorami 1
  • B. Ghahraman 2
1 Ph.D. Student in Irrigation and drainage, Department of Water Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
2 Professor, Department of Water Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده [English]

Uncertainty is the measure of the reliability associated with a particular set of results. There are a lot of effective parameters in water movement through the unsaturated zone and obtaining measurement or estimation of them are difficult and have a kind of uncertainty.In this study, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. Richards’ equation as a certain model was solved numerically .To estimate uncertainty in model; input parameters (θs, θr, Ks, α and n) were introduced as fuzzy parameters. After introducing suitable fuzzy membership functions for input parameters, at different β level cuts in input parameters, there will be boundaries for each parameter, then the mathematical operation on fuzzy sets are performed at different β- cut levels and result interval boundaries for the moisture in specific time and location. Corresponding to different β- cuts, fuzzy membership functions were derived for soil moisture at any time and depth. The results showed that uncertainty in simulating soil moisture profile is minimum in saturated phase and it is maximum in advance phase, that’s because of maximum number of parameters that taking part with maximum uncertainty in this phase. The shape of fuzzy membership function for soil moisture in specific time is varying for different depths because the rule of effective initial parameters in any time and depth are different.

کلیدواژه‌ها [English]

  • Unsaturated zone
  • Numerical Solution
  • Richard’s equation
  • HYDRUS
Bardossy A, Bronster A, Merz B (1995) 1, 2 and 3-dimensional modeling of water movement in the unsaturated soil matrix using a fuzzy approach. Advances in Water Resources 18(4):237-251
Bearnard F (2003) Fuzzy environmental decision-making: Applications to air pollution, Atmospheric Environment 37(14):1865–1877
Carroll RWH, Warwick JJ (2001) Uncertainty analysis of the Carson River mercury transport model. Ecological Modelling 137:211-224
Clapp RB, Hornburger GM (1987) Empirical equations for some soil hydraulic properties. Water Resources Research 14:601-604
Copty NK, Findikakis AN (2000) Quantitative estimate of uncertainty in the evaluation of ground water remediation Schemes. Ground Water 38:29-37
De Jong R (1982) Assessment of empirical parameters that describe soil water characteristics. Canadian Biosystems Engineering 24:65-70
Dixon B (2005) Groundwater vulnerability mapping: A GIS and fuzzy rule based integrated tool. Applied Geography 25:327–347
Dou C, Woldt W, Bogardi I (1999) Fuzzy rule based approach to describe solute transport in unsaturated zone. Journal of Hydrology 220:74–85
Dou C, Woldt W, Bogardi I, Dahab M (1995) Steady state groundwater flow simulations with imprecise parameters. Water Resources Research 31:2709–2719
Dubois D, Prade H (1980) Fuzzy sets and systems: theory and application. Academic, San Diego, 144p
Eymard R, Gutnic M, Hilhorst D (1999) The finite volume method for Richards equation. Computational  Geosciences 3(3):259–294
Haverkamp R, Vanclin M, Touma J, Wierenga PJ, Vachaud G (1997) A comparison of numerical simulation models for one-dimensional infiltration. Soil Science Society of America Journal (41):285-294
Li J, Huang GH, Zeng G, Maqsood I, Huang Y (2007) An integrated fuzzy stochastic modeling approach for risk assessment of groundwater contamination. Journal of Environmental Engineering 82:173–188
Nasiri F, Huang G, Fuller N (2007) Prioritizing groundwater remediation policies: A fuzzy compatibility analysis decision aid. Journal of Environmental Engineering 82:13–23
Rawls WJ, Brakensik DL, Saxton KE(1982) Estimation of soil water properties. Transactions of the American Society of Agricultural Enginnering 25:1316-1982
Richards LA (1931) Capillary conduction of liquids through porous media. Journal of Applied Physics 1:318-333
Rubio E, Hall JW, Anderson MG (2004) Uncertainty analysis in a slope hydrology and stability model using probabilistic and imprecise information. Computers and Geotechnics Journal 31:529–536
Russo D, Bouton M (1992) Statistical analysis of spatial variability. Water Resources Research 28:1911–1925
Sax T, Isakov V (2003) A case study for assessing Uncertainty in local – scale regulatory air quality modeling applications. Atmospheric Environment 37:3481-3489
Schaap MG, Leij FJ, van Genuchten MTh (2001) Rosetta: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer function. Journal of  Hydrology 251:163-176
Schulz K, Huwe B (1997) Water flow modeling in the unsaturated zone with imprecise parameters using a fuzzy approach. Journal of Hydrology 201:211-229
Schulz K, Huwe B (1999) Uncertainty and sensitivity analysis of water transport modelling in a layered soil profile using fuzzy set theory. Journal of Hydroinformatics. 01(2):127-138
Shafiei M, Ghahraman B, Saghafian B, Davary K, Pande S, Vazifedoust M (2014) Uncertainty assessment of the agro-hydrological SWAP model application at field scale: A case study in a dry region. Agricultural Water Management 146(12):324-334
Simunek J, Sejna M, van Genuchten MTh (1999) The Hydrus-2D software package for simulating two-dimensional movement of water, heat, and multiple solutes in variably saturated media. Version 2.0, IGWMC - TPS - 53, International Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado, 251p
Simunek J, Van Genuchten MTh, Sejna M (2006) The HYDRUS software package for simulating the two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Version 01, Technical Manual. PC Progress, Prague, Czech Republic, 213p
 Smith RI, Fowler D, Sutton MA, Flecyhard C, Coyle M (1999) Regional estimation of pollutant gas dry deposition in the UK. Model description, sensitivity analyses and outputs. Atmospheric Environment 34:3757-3777
Smith RE, Parlange JY (1978) A parameter-efficient hydrologic infiltration model. Water Resources Research 14(3):533–538
Subia SR, Ingber MS, Martinez MJ (1994) A three– dimensional boundary element method for steady unsaturated quasi-linear flow in porous media. Water Resources Research 30(7):2097-2104
Tracy FT (2011) Analytical and numerical solutions of Richards' equation with discussions on relative hydraulic conductivity. In Lakshmanan E (ed) Hydraulic Conductivity - Issues, Determination and Applications, ISBN: 978-953-307-288-3, 203-222p
Uricchio VF, Giordano R, Lopez N (2004) A fuzzy knowledge-based decision support system for groundwater pollution risk evaluation. Journal of Environmental Management 73:189–197
Verma P, Singh P, George KV, Singh HV, Devotta S, Singh RN (2009) Uncertainty analysis of transport of water and pesticide in an unsaturated layered soil profile using fuzzy set theory. Applied Mathematical Modelling 33:770-782
Warwick JJ, Cale WG (1986) Effect of parameter uncertainty in stream modeling. Journal of Environmental Engineering 112(3):479–489
Woldt W, Daheb M, Bogardi I, Dou C (1996) Management of diffuse pollution in groundwater under imprecise conditions using fuzzy models Water Science and Technology 33:249–257
Yeanan A, Williamson DG, Graettinger AJ (2002) Uncertainty analysis in air dispersion modeling, Environmental Modelling and Software 17:639-649
Zadeh LA (1965) Fuzzy sets. Information and Control 8(3):338–353