quantitative modeling of nitrate distribution in the ardabil plain aquifer using fuzzy logic

Authors

مهدی کرد

استادیار گروه زمین شناسی، دانشکدۀ علوم پایه، دانشگاه کردستان اصغر اصغری مقدم

استاد گروه زمین شناسی، دانشکدۀ علوم طبیعی، دانشگاه تبریز محمد نخعی

دانشیار گروه زمین شناسی، دانشکدۀ علوم زمین، دانشگاه خوارزمی

abstract

introduction the ardabil plain aquifer, with area about 900 km2, has high concentration amounts of nitrate in some parts. nowadays, nitrate pollution in groundwater due to the widespread application of fertilizers and increasing of drinking water demand, has encountered consumers with problem. the adverse health effects of high nitrate levels in drinking water have been well documented. in the last two decades use of fuzzy logic has considered to simulate of environmental process because of complexity in modeling domain and uncertainty in data. most of these research studies has profited from advantages of fuzzy logic beside other scientific methods. in previous published academic researches which investigated vulnerability of aquifer by fuzzy logic, it has been concluded that data clustering and determination of bounds between these clusters is a matter of importance and the efficiency of fuzzy logic is higher than traditional methods. reviewing the previous records indicates that there is not any literature about modeling of nitrate in ardabil plain. so in this study distribution of nitrate in ardabil plain aquifer has been estimated using fuzzy logic modeling and the performance of this method has been compared with kriging. material and methods the study area is located between latitude 38°00′ and 38°30′ and longitude 48°00′ and 48°40′ and it covers an area of approximately 900 km2. in order to spatial distribution modeling of nitrate concentration in ardabil plain, a total of 61 wells were sampled for chemical analyses on november, 2011. in this study 75% and 25% of samples were used for calibration and verification, respectively. fuzzy logic contrary to classic sets, that their members are completely belong to them, in fuzzy sets the members have membership grades between 0 and 1. one of the applications of fuzzy theory is modeling. in order to modeling by fuzzy logic, first input data are shown as fuzzy membership functions, then these membership functions are related to output data via definition of fuzzy rules. sugeno model is used in process of this kind of modeling which consists of three stages: 1- clustering, 2- identification of rules and 3- parameter estimation. to determine the optimum number of clusters, the software of fuzme has been applied. after the determination of classes, inputs of model were related to the outputs by definition of the if-then fuzzy rules. in the last step, least square errors were minimized to calibrate model. kriging kriging is a geostatistics interpolation method which is an efficient linear unbiased estimator. after the examination of normality of data and using normalization for data without normal distribution, the best experimental and theoretical variogram basis isotropic or anisotropic properties of data plotted by gs+ software. as a result the best chosen variogram was exponential with nugget effect of 0.09 and sill about 0.50. discussion of results & conclusions in this study longitude and latitude have considered as inputs and nitrate concentrations have kept for output of model. for the reason that the utm amounts were large numbers, in the beginning the inputs normalized between 0 and 1 then they were classified in six clusters by fuzzy c-mean clustering method. since the number of rules in this type of modeling is equal to the clusters, therefore the set of inputs was related to the set of outputs via defining six rules and the parameters of model were estimated by the running of the model. the calibrated parameters of input and output membership functions are given in table (1). table 1- the optimized parameters of input membership functions and output linear functions cluster input1 input2 out put σ c σ c α β ε 1 0.1672 0.3313 0.1768 0.6902 44.83 9.937 -3.126 2 0.1256 0.5027 0.1243 0.5807 566.4 -317.8 -119.4 3 0.1287 0.6495 0.2049 0.4377 -19.18 66.09 16.72 4 0.1143 0.4066 0.1598 0.6709 127.6 -319.4 242.1 5 0.1369 0.6086 0.1599 0.5013 132.5 -121.5 -105.9 6 0.0492 0.5478 0.08954 0.8856 -244 -265.1 392.4 to do the verification of model a total of 16 separated samples were used and its results were compared with that of kriging method. for this purpose root mean square error (rmse), mean absolute error (mae) and coefficient of determination (r2) were computed which is presented in table (2). table 2- statistical characteristics of used data for verification r2 rmse mae std mean model 0.916 1.6940 1.3982 5.063 7.99 fuzzy logic 0.517 4.3549 2.9677 2.594 5.82 kriging - - - 5.57 8.65 measured according to reported results in table (2), purposed model showed better results than kriging method, so to generate the nitrate distribution map, the verified fuzzy model was run and final result is shown in figure (1). figure 1- spatial distribution map of nitrate in ardabil plain aquifer the reliability of spatial distribution maps of pollutant is very important in water resources management. basically, the geostatistics interpolation methods especially kriging are used to generate spatial distribution data. according to the results, the used fuzzy model was very efficient in estimating of nitrate concentrations in the study area. the final output of the model shows that the nitrate concentrations in some parts of north and south –west of the plain is higher than 10 mg which these parts occupied about 17% of aquifer area. the places with high amounts of nitrate around ardabil city had full conformity with urban waste water, thus with strong probability nitrate pollution could be related to waste water. also, high concentrations of nitrate in the north margin of the plain are in conformity with landfill which it can be considered as cause of nitrate pollution at that area likely.

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محیط شناسی

جلد ۴۱، شماره ۱، صفحات ۶۷-۷۹

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h s t u d i e s h a s p r o f i t e d f r o m a d v a n t a g e s o f f u z z y l o g i c b e s i d e o t h e r s c i e n t i f i c m e t h o d s . r n i n p r e v i o u s p u b l i s h e d a c a d e m i c r e s e a r c h e s w h i c h i n v e s t i g a t e d v u l n e r a b i l i t y o f a q u i f e r b y f u z z y l o g i c ' , ' i t h a s b e e n c o n c l u d e d t h a t d a t a c l u s t e r i n g a n d d e t e r m i n a t i o n o f b o u n d s b e t w e e n t h e s e c l u s t e r s i s a m a t t e r o f i m p o r t a n c e a n d t h e e f f i c i e n c y o f f u z z y l o g i c i s h i g h e r t h a n t r a d i t i o n a l m e t h o d s . r n r e v i e w i n g t h e p r e v i o u s r e c o r d s i n d i c a t e s t h a t t h e r e i s n o t a n y l i t e r a t u r e a b o u t m o d e l i n g o f n i t r a t e i n a r d a b i l p l a i n . s o i n t h i s s t u d y d i s t r i b u t i o n o f n i t r a t e i n a r d a b i l p l a i n a q u i f e r h a s b e e n e s t i m a t e d u s i n g f u z z y l o g i c m o d e l i n g a n d t h e p e r f o r m a n c e o f t h i s m e t h o d h a s b e e n c o m p a r e d w i t h k r i g i n g . r n x a 0 r n m a t e r i a l a n d m e t h o d s r n t h e s t u d y a r e a i s l o c a t e d b e t w e e n l a t i t u d e 3 8 ° 0 0 ′ a n d 3 8 ° 3 0 ′ a n d l o n g i t u d e 4 8 ° 0 0 ′ a n d 4 8 ° 4 0 ′ a n d i t c o v e r s a n a r e a o f a p p r o x i m a t e l y 9 0 0 k m 2 . i n o r d e r t o s p a t i a l d i s t r i b u t i o n m o d e l i n g o f n i t r a t e c o n c e n t r a t i o n i n a r d a b i l p l a i n ' , ' a t o t a l o f 6 1 w e l l s w e r e s a m p l e d f o r c h e m i c a l a n a l y s e s o n n o v e m b e r ' , ' 2 0 1 1 . i n t h i s s t u d y 7 5 % a n d 2 5 % o f s a m p l e s w e r e u s e d f o r c a l i b r a t i o n a n d v e r i f i c a t i o n ' , ' r e s p e c t i v e l y . r n x a 0 r n f u z z y l o g i c r n c o n t r a r y t o c l a s s i c s e t s ' , ' t h a t t h e i r m e m b e r s a r e c o m p l e t e l y b e l o n g t o t h e m ' , ' i n f u z z y s e t s t h e m e m b e r s h a v e m e m b e r s h i p g r a d e s b e t w e e n 0 a n d 1 . o n e o f t h e a p p l i c a t i o n s o f f u z z y t h e o r y i s m o d e l i n g . i n o r d e r t o m o d e l i n g b y f u z z y l o g i c ' , ' f i r s t i n p u t d a t a a r e s h o w n a s f u z z y m e m b e r s h i p f u n c t i o n s ' , ' t h e n t h e s e m e m b e r s h i p f u n c t i o n s a r e r e l a t e d t o o u t p u t d a t a v i a d e f i n i t i o n o f f u z z y r u l e s . s u g e n o m o d e l i s u s e d i n p r o c e s s o f t h i s k i n d o f m o d e l i n g w h i c h c o n s i s t s o f t h r e e s t a g e s : 1 ' , ' c l u s t e r i n g ' , 2 , ' i d e n t i f i c a t i o n o f r u l e s a n d 3 ' , ' p a r a m e t e r e s t i m a t i o n . r n t o d e t e r m i n e t h e o p t i m u m n u m b e r o f c l u s t e r s ' , ' t h e s o f t w a r e o f f u z m e h a s b e e n a p p l i e d . x a 0 x a 0 x a 0 r n a f t e r t h e d e t e r m i n a t i o n o f c l a s s e s ' , ' i n p u t s o f m o d e l w e r e r e l a t e d t o t h e o u t p u t s b y d e f i n i t i o n o f t h e i f ' , ' t h e n f u z z y r u l e s . i n t h e l a s t s t e p ' , ' l e a s t s q u a r e e r r o r s w e r e m i n i m i z e d t o c a l i b r a t e m o d e l . r n x a 0 r n k r i g i n g r n k r i g i n g i s a g e o s t a t i s t i c s i n t e r p o l a t i o n m e t h o d w h i c h i s a n e f f i c i e n t l i n e a r u n b i a s e d e s t i m a t o r . a f t e r t h e e x a m i n a t i o n o f n o r m a l i t y o f d a t a a n d u s i n g n o r m a l i z a t i o n f o r d a t a w i t h o u t n o r m a l d i s t r i b u t i o n ' , ' t h e b e s t e x p e r i m e n t a l a n d t h e o r e t i c a l v a r i o g r a m b a s i s i s o t r o p i c o r a n i s o t r o p i c p r o p e r t i e s o f d a t a p l o t t e d b y g s + s o f t w a r e . a s a r e s u l t t h e b e s t c h o s e n v a r i o g r a m w a s e x p o n e n t i a l w i t h n u g g e t e f f e c t o f 0 . 0 9 a n d s i l l a b o u t 0 . 5 0 . r n x a 0 r n d i s c u s s i o n o f r e s u l t s & c o n c l u s i o n s r n i n t h i s s t u d y l o n g i t u d e a n d l a t i t u d e h a v e c o n s i d e r e d a s i n p u t s a n d n i t r a t e c o n c e n t r a t i o n s h a v e k e p t f o r o u t p u t o f m o d e l . f o r t h e r e a s o n t h a t t h e u t m a m o u n t s w e r e l a r g e n u m b e r s ' , ' i n t h e b e g i n n i n g t h e i n p u t s n o r m a l i z e d b e t w e e n 0 a n d 1 t h e n t h e y w e r e c l a s s i f i e d i n s i x c l u s t e r s b y f u z z y c ' , ' m e a n c l u s t e r i n g m e t h o d . s i n c e t h e n u m b e r o f r u l e s i n t h i s t y p e o f m o d e l i n g i s e q u a l t o t h e c l u s t e r s ' , ' t h e r e f o r e t h e s e t o f i n p u t s w a s r e l a t e d t o t h e s e t o f o u t p u t s v i a d e f i n i n g s i x r u l e s a n d t h e p a r a m e t e r s o f m o d e l w e r e e s t i m a t e d b y t h e r u n n i n g o f t h e m o d e l . t h e c a l i b r a t e d p a r a m e t e r s o f i n p u t a n d o u t p u t m e m b e r s h i p f u n c t i o n s a r e g i v e n i n t a b l e ( 1 ) . r n x a 0 r n t a b l e 1 ' , ' t h e o p t i m i z e d p a r a m e t e r s o f i n p u t m e m b e r s h i p f u n c t i o n s a n d o u t p u t l i n e a r f u n c t i o n s r n r n r n r n r n r n c l u s t e r r n r n r n i n p u t 1 r n r n r n i n p u t 2 r n r n r n o u t p u t r n r n r n r n r n σ r n r n r n c r n r n r n σ r n r n r n c r n r n r n α r n r n r n β r n r n r n ε r n r n r n r n r n 1 r n r n r n 0 . 1 6 7 2 r n r n r n 0 . 3 3 1 3 r n r n r n 0 . 1 7 6 8 r n r n r n 0 . 6 9 0 2 r n r n r n 4 4 . 8 3 r n r n r n 9 . 9 3 7 ' , ' 3 . 1 2 6 r n r n r n r n r n 2 r n r n r n 0 . 1 2 5 6 r n r n r n 0 . 5 0 2 7 r n r n r n 0 . 1 2 4 3 r n r n r n 0 . 5 8 0 7 r n r n r n 5 6 6 . 4 ' , ' 3 1 7 . 8 ' , ' 1 1 9 . 4 r n r n r n r n r n 3 r n r n r n 0 . 1 2 8 7 r n r n r n 0 . 6 4 9 5 r n r n r n 0 . 2 0 4 9 r n r n r n 0 . 4 3 7 7 ' , ' 1 9 . 1 8 r n r n r n 6 6 . 0 9 r n r n r n 1 6 . 7 2 r n r n r n r n r n 4 r n r n r n 0 . 1 1 4 3 r n r n r n 0 . 4 0 6 6 r n r n r n 0 . 1 5 9 8 r n r n r n 0 . 6 7 0 9 r n r n r n 1 2 7 . 6 ' , ' 3 1 9 . 4 r n r n r n 2 4 2 . 1 r n r n r n r n r n 5 r n r n r n 0 . 1 3 6 9 r n r n r n 0 . 6 0 8 6 r n r n r n 0 . 1 5 9 9 r n r n r n 0 . 5 0 1 3 r n r n r n 1 3 2 . 5 ' , ' 1 2 1 . 5 ' , ' 1 0 5 . 9 r n r n r n r n r n 6 r n r n r n 0 . 0 4 9 2 r n r n r n 0 . 5 4 7 8 r n r n r n 0 . 0 8 9 5 4 r n r n r n 0 . 8 8 5 6 ' , 2 4 4 , ' 2 6 5 . 1 r n r n r n 3 9 2 . 4 r n r n r n r n r n r n x a 0 r n t o d o t h e v e r i f i c a t i o n o f m o d e l a t o t a l o f 1 6 s e p a r a t e d s a m p l e s w e r e u s e d a n d i t s r e s u l t s w e r e c o m p a r e d w i t h t h a t o f k r i g i n g m e t h o d . f o r t h i s p u r p o s e r o o t m e a n s q u a r e e r r o r ( r m s e ) ' , ' m e a n a b s o l u t e e r r o r ( m a e ) a n d c o e f f i c i e n t o f d e t e r m i n a t i o n ( r 2 ) w e r e c o m p u t e d w h i c h i s p r e s e n t e d i n t a b l e ( 2 ) . r n x a 0 r n t a b l e 2 ' , ' s t a t i s t i c a l c h a r a c t e r i s t i c s o f u s e d d a t a f o r v e r i f i c a t i o n r n r n r n r n r n r n r 2 r n r n r n r m s e r n r n r n m a e r n r n r n s t d r n r n r n m e a n r n r n r n m o d e l r n r n r n r n r n 0 . 9 1 6 r n r n r n 1 . 6 9 4 0 r n r n r n 1 . 3 9 8 2 r n r n r n 5 . 0 6 3 r n r n r n 7 . 9 9 r n r n r n f u z z y l o g i c r n r n r n r n r n 0 . 5 1 7 r n r n r n 4 . 3 5 4 9 r n r n r n 2 . 9 6 7 7 r n r n r n 2 . 5 9 4 r n r n r n 5 . 8 2 r n r n r n k r i g i n g ' , ' ' , ' ' , ' 5 . 5 7 r n r n r n 8 . 6 5 r n r n r n m e a s u r e d r n r n r n r n r n r n x a 0 r n a c c o r d i n g t o r e p o r t e d r e s u l t s i n t a b l e ( 2 ) ' , ' p u r p o s e d m o d e l s h o w e d b e t t e r r e s u l t s t h a n k r i g i n g m e t h o d ' , ' s o t o g e n e r a t e t h e n i t r a t e d i s t r i b u t i o n m a p ' , ' t h e v e r i f i e d f u z z y m o d e l w a s r u n a n d f i n a l r e s u l t i s s h o w n i n f i g u r e ( 1 ) . r n x a 0 r n f i g u r e 1 ' , ' s p a t i a l d i s t r i b u t i o n m a p o f n i t r a t e i n a r d a b i l p l a i n a q u i f e r r n x a 0 r n t h e r e l i a b i l i t y o f s p a t i a l d i s t r i b u t i o n m a p s o f p o l l u t a n t i s v e r y i m p o r t a n t i n w a t e r r e s o u r c e s m a n a g e m e n t . b a s i c a l l y ' , ' t h e g e o s t a t i s t i c s i n t e r p o l a t i o n m e t h o d s e s p e c i a l l y k r i g i n g a r e u s e d t o g e n e r a t e s p a t i a l d i s t r i b u t i o n d a t a . a c c o r d i n g t o t h e r e s u l t s ' , ' t h e u s e d f u z z y m o d e l w a s v e r y e f f i c i e n t i n e s t i m a t i n g o f n i t r a t e c o n c e n t r a t i o n s i n t h e s t u d y a r e a . x a 0 r n t h e f i n a l o u t p u t o f t h e m o d e l s h o w s t h a t t h e n i t r a t e c o n c e n t r a t i o n s i n s o m e p a r t s o f n o r t h a n d s o u t h – w e s t o f t h e p l a i n i s h i g h e r t h a n 1 0 m g w h i c h t h e s e p a r t s o c c u p i e d a b o u t 1 7 % o f a q u i f e r a r e a . r n t h e p l a c e s w i t h h i g h a m o u n t s o f n i t r a t e a r o u n d a r d a b i l c i t y h a d f u l l c o n f o r m i t y w i t h u r b a n w a s t e w a t e r ' , ' t h u s w i t h s t r o n g p r o b a b i l i t y n i t r a t e p o l l u t i o n c o u l d b e r e l a t e d t o w a s t e w a t e r . a l s o ' , ' h i g h c o n c e n t r a t i o n s o f n i t r a t e i n t h e n o r t h m a r g i n o f t h e p l a i n a r e i n c o n f o r m i t y w i t h l a n d f i l l w h i c h i t c a n b e c o n s i d e r e d a s c a u s e o f n i t r a t e p o l l u t i o n a t t h a t a r e a l i k e l y . 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