کاهش متغیرهای الگوی بار نیتروژن ورودی به آب رودخانه با روش تحلیل حساسیت واریانس مبنا مطالعه موردی: حوضه آبریز رودخانه توید

نوع مقاله : مقالات پژوهشی

نویسندگان

دانشگاه صنعتی شاهرود

چکیده

شناخت و کنترل متغیرهای موثر بر نیتروژن ورودی به منابع آب به عنوان یکی از عوامل تهدید کننده حیات انسان و آبزیان اهمیت دارد. متغیرهای موثر را می‌توان با فنون ریاضی و ابداع راهکارهای شبیه‌سازی رایانه‌ای، شناسایی و از عوامل با اثرات ناچیز صرف نظر کرد تا بتوان منابع مالی را برای کنترل تعداد معدودی از عوامل بهینه صرف نمود. الگو‌های متعددی برای برآورد میزان این ترکیبات ساخته شده ‌است. در این راستا از الگوی پرکاربرد (INCA-N) Integrated Nitrogen in Catchments، به‌منظور انجام تحلیل حساسیت متغیرها و کاهش تعداد آن‌ها در این مقاله استفاده شده است. INCA-N شامل صدها متغیر ورودی است. لذا شناسایی متغیرهای بی‌تاثیر یا کم تاثیر حائز اهمیت است. روش تحلیل حساسیت واریانس- مبنا با شاخص‌حساسیت اصلی به‌خوبی می‌تواند متغیرهای مهم را شناسایی و حساسیت خروجی الگو را ارزیابی کند. این مقاله ضمن معرفی روش واریانس مبنا و برآورد شاخص‌های حساسیت باروش مونت کارلو و تولید اعداد شبه‌تصادفی، به تحلیل حساسیت خروجی الگو INCA-N و کاهش متغیرها در رودخانه توید می‌پردازد. نتایج تحلیل حساسیت در حجم نمونه بهینه نشان داد که چهار ‌متغیر (میزان جذب ‌نیترات گیاهان، نرخ نیترات‌زدایی، آلی‌سازی و معدنی‌سازی) از هفت متغیر الگو INCA-N کفایت می‌کند. سه متغیر نیتروژن هوا، برداشت آمونیاک توسط گیاه و بیشینه برداشت نیتروژنی غیرضروری هستند. این چهار متغیر ضروری به ترتیب دارای اثر اصلی و اثرکل (44/0، 49/0)، (189/0،248/0)، (182/0، 227/0)، (072/0، 105/0) هستند. اثرات متقابل بین متغیرها ضعیف (حداکثر 059/0) و قابل چشم‌پوشی است. بنابراین روش تحلیل حساسیت کارایی خوبی در کاهش متغیرهای این پدیده دارد.

کلیدواژه‌ها


عنوان مقاله [English]

Reduction of variable nitrogen river water loading model by variance based sensitivity analysis, Case Study: Tweedriverbasin

نویسندگان [English]

  • majid janfada
  • D. Shahsavani
Shahrood University of Technology
چکیده [English]

Introduction: The nitrogen cycle may be affected by chemical fertilization and industrial waste water. Nitrate can affect the human body through water and food, which can be transformed into nitrate and nitrosamine as a threat for humans and aquatic life. Therefore, detecting the influential elements and factors on this cycle, are essential from the environmental protection point of view. Many of scientists utilize mathematical models for these kind of problems. These models encompass linear and nonlinear differential equations that aresolved by numerical computer cods. The numerical codes are called “Deteministic computer models”, and running the model with different input values is called a computer experiment. One of the most famous models for the estimation of nitrogen river load is INCA-N (Integrated Nitrogen in Catchments).
Materials and Methods: INCA-N is a semi-distributed, process-based deterministic model of the flow of water and nitrogen through catchments. It simulates the key factors and processes that affect the amount of NO3 and NH4 stored in the soil and groundwater systems, and it feeds the outputs from these systems into a multi-reach river model. INCA-N has different input variables, thus detection of inactive variables of INCA-N is important. Because of reducing the input variables and simplifying of model, sensitivity analysis methods are used.
Sensitivity analysis involves sampling based, screening based and monte-carlo based and variance based method. Variance based method, which us used in this paper, detectsthe important variable and interaction effects. The main effect (first-order index) and total effect are most popular and important indices in variance based sensitivity analysis. These indices are multiple integrals based on the concepts of conditional mathematical expectation and conditional variance.The first-order index represents the main effect contribution of each input factor to the variance of the output. The total effect index accounts for the total contribution to the output variation due to factor Xi, i.e. its first-order effect plus all higher-order interaction effects. These indices are defined based on multidimensional integral which is estimated by simulation techniques.
In this paper, after introducing variance based approach and estimation of sensitivity indices with Monte Carlo and quasi random number, our attention is focused onsensitivity analysis of ofINCA-N model in the Tweed river. In this study the derived output is the average annual riverine load of inorganic nitrogen over a period of seven years.
Results and Discussion: The results of sensitivity analysis in optimized sample size showed that four variables, out of seven, of INCA-N are important:
1." Plant nitrate uptake." The average main effect and total effect of this variable are 0.44 and 0.49, respectively. The difference between the total effect and main effect, which is 0.051, indicates that this factor does not have any significant interaction with other input variables in the model.
2. "Denitrification rate". The mean and standard deviation for the main effect were 0.247 and 0.189, whereasthese two measures for the total effect are 0.248 and 0.366, respectively.
3. " Immobilization ". The mean and standard deviation of immobilization were 0.182 and 0.787 for the main effect, and they are 0.227 and 0.3736 for the total effect respectively.
4. "Mineralization rate". The mean and standard deviation of this variable were 0.072 and 0.268 for the main effect, and 0.106 and 0.391 for the total effect,respectively .
The main and total effect of thesefour variables are (0.44,0.49), (0.247,0.248), (0.182,0.227), (0.072,0.106). It can be mentioned that, the interaction between these variable are so weak (maximum= 0.059). Three other variables nitrogen fixation, ammonium planet uptake and maximum nitrogen uptake is not important. Thus the sensitivity analysis method has good efficiency in the reduction of variation.
Conclusions: To manage the riverine load of inorganic nitrogen in the Tweed River at least fourfactors, including nitrate uptake rate by plants, denitrification rates, immobilization and mineralization, should be controlled. The variance based method makes it possible to detect the important variables. In the other words, the sensitivity analysis lts of INCA-N model showed that for controlling the nitrogen entering the Tweed River, at least three factors of "plants nitrate uptake," "denitrification rate" and "immobilization" should be taken into consideration. In addition to these three factors, mineralization can be considered as the fourth factor affecting the nitrogen load.

کلیدواژه‌ها [English]

  • Deterministic computer models
  • Nitrogen
  • dimension reduction
  • Monte Carlo method
  • INCA-N model
1- Archer G.E.B. Saltelli A., and Sobol I.M. 1997. Sensitivity Measures, Anova-Like Techniques and the Use of Bootstrap. Statistical Computation. 58: 99-120.
2- Bhattacharrya K.G., and Gupta S.S. 2006. Pb (II) uptake by kaolinite and montmorillonite in aqueous medium: Influence of acid activation of the clays. Colloids Surface. 277:191-200.
3- Campolongo F., Cariboni J., and Saltelli A. 2007. An effective screening design for sensitivity analysis of large models. Environmental Modelling and Software. 22:1509–1518.
4- Cuiker R.I., Schaibly J.H., Schuler A.G. 1975. Study of the Sensitivity of coupled Reaction System to Uncertainties in Rate Coefficient. III Analysis of the Approximations. Chemical Physics. 63:1140–1149.
5- Cukier R.I., Fortuin C.M., Schuler K.E., Petschek A.G., and Schaibly J.H. 1973. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients in theory. Chemical Physics. 59: 3873–3878.
6- Cukier R., Levine H., and Shuler K. 1978. Nonlinear sensitivity analysis of multiparameter model systems, Computational Physics. 26:1–42.
7- Helton J.C., Johnson J.D., Salaberry C.J., Storlie C.B. 2006. Survey of sampling based methods for uncertainty and sensitivity analysis. Reliability Engineering and System Safety. 91:1175–1209.
8- Homma T., and Saltelli. A. 1996. Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering and System Safety. 52:1–17.
9- Hornberger G., and Spear, R. 1981. An approach to the preliminary analysis of environmental systems. Environmental Management. 7: 7–18.
10- Iman R., and Hora S. 1990. A robust measure of uncertainty importance for use in fault tree system analysis. Risk Analysis. 10(3):401–403.
11- Ishigami T., and Homma T. 1996. An importance qualification technique in uncertainty analysis for compute models, in: Proceedings of the Isuma ’90. First International Symposium on Uncertainty Modelling and Analysis, University of Maryland, 3–5 December.
12- Jarvie H. P., Wade A.J., Butterfield D., Whitehead P.G., Tindall C. I., Virtue, W.A., Dryburgh W. and McCraw A. 2002. Modelling nitrogen dynamics and distributions in the River Tweed, Scotland: an application of the INCA-N model, Hydrol. Earth Sys. Sci. 6:443-453.
13- Karaivanova A., Dimov I., and Ivanovska S. 2000. A Quasi-Monte Carlo Method for Integration with Improved Convergence.
14- Krzykacz-Hausmann B.1990. Gesellschaft fuer Reaktor Sicherheit (GRS) MbH. Technical Report GRS-A-1700, Garching.
15- Levy G., An introduction to quasi-random numbers. 2002. NAG Ltd, Oxford, UK
16- McKay M., 1996. Variance-based methods for assessing uncertainty importance in nureg-1150 analysis. Technical Report LA-UR-96-2695, 1, Los Alamos Laboratories.
17- Medici C., Bernal S., Butturini A., Sabater F., Martin M., Wade A.J., and Frances F. 2010. Modelling the inorganic nitrogen behaviour in a small Mediterranean forested catchment, Fuirosos (Catalonia). Hydrology and Earth System Sciences. 14 (2):223-237.
18- Mishra P.C., and Patel R.K. 2009. Use of agricultural waste for the removal of nitrate- nitrogen from aqueous medium. Environmental Management. 90:519-522.
19- Morris M.D. 1991. Factorial sampling plans for preliminary computational experiments. Technometrics. 33:161–174.
20- Ozturk N., and Ennil Kose T. 2008. A kinetic study of nitrite adsorption onto sepiolite and powdered activated carbon. Desalination. 223:174-179.
21- Ranzin M., Forti M.C., Whitehead P.G., Arcova F.C.S., Cicco V.de and Wade A.J. 2007. Integrated Nitrogen Catchment model (INCA-N) applied to a tropical catchment in the Atlantic Forest, Sao Paulo, Brazil. Hydrology and Earth System Sciences. 11(1):pp.614-622.
22- Saltelli A., Sobol’ IM., 1995. About the use of rank transformation in sensitivity analysis model. Reliable Eng Syst. Saf. 50:225–39.
23- Saltelli A, Tarantola S, Chan K. A. 1999. quantitative model-independent method for global sensitivity analysis of model output, J. of Technometrics. 41(1).
24- Saltelli A., Andres T.H. Homma, T. 1993. Some new techniques in sensitivity analysis of model output. Comput. Statist. Data Anal. 15:211–238.
25- Saltelli, A. 2002. Sensitivity Analysis for Importance Assessment. Risk Analysis. 22:3.
26- Saltelli A., Annoni P., Azzini I., Campolongo F., Ratto M., Tarantola S., 2010. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index, J. Computer Physics Communications. 181:259–270.
27- Saltelli A., Ratto M., Andres T., Campolongo F., Cariboni J., Gatelli D., Saisana M., Tarantola S. 2008. Global sensitivity analysis The Primer. John Wiley & Sons Ltd. 1.
28- Saltelli A., Sobol’ I.M. 1995. About the use of rank transformation in sensitivity analysis of model output Reliability Engrg. Syst. Safety. 50:225–239.
29- Saltelli A., Tarantola S., Campolongo F., Ratto M., 2004. Sensitivity Analysis in Practice. John Wiley & Sons Ltd. 1.
30- Santner T.J., Williams B.J., Notz W. I. 2003. The Design and Analysis of Computer Experiments. Springer, New York . 1.
31- Shahsavani D., Grimvall A. 2011. Variance-based sensitivity analysis of model outputs using surrogate models. Environmental Modelling and Software. 26(6): 723-730.
32- Sobol I.M. 1998. On quasi-Monte Carlo integrations. Mathematics and Computers in Simulation. 47, 103±112.
33- Sobol I. M. 1993. Sensitivity analysis for non-linear mathematical models. Mathematical Modelling and Computational Experiment. 1:407–414. English translation of Russian original paper Sobol’ (1990).
34- Tarantola S. Gatellia D., Mara T. A. 2006. Random balance designs for the estimation of first order global sensitivity indices. Reliability engineering and system safety. 91(6):717-727.
35- Wade A. J., Durand P., Beaujouan V., Wessel W. W., Raat K. J., Whitehead P. G., Butterfield D., Rankinen K., Lepisto A. 2002. A nitrogen model for European catchments: INCA-N, new model structure and equations. Hydrology and Earth System Sciences. 6:559-582.
36- Whitehead P. G., Wilson E. J., Butterfield D. 1998a. A semi-distributed nitrogen model for multiple source assessments in catchments (INCA-N): Model structure and process equations. Science of the Total Environment. 210/211:547-558.
37- Whitehead P., Butterfield, D. and Wade, A. 2008. Potential impacts of climate change on river water quality, Environment Agency, Science Report – SC070043/SR1.
38- Whitehead., P. 2007. A Water Quality Modelling Study of Roşia Montană and the Abrud, Aries and Mures River Systems: Assessing Restoration Strategies and the Impacts of Potential Pollution Events model systems, Computational Physics. 26:1–42.
39- Xing X., Gao B., Yue Q., and Zhong Q.Q., 2010. Preparation of agricultural by-product based anion exchanger and its utilization for nitrate and phosphate removal. Bioresource Technology. 101: 8558-8564