Analysis of Water Parameters Using Daubechies Wavelet (Level 5) (Db5)

Transcription

1 American Journal of Mathematic and Statitic, (3): -3 DOI:.93/j.ajm.3.8 Analyi of Water Parameter Uing Daubechie Wavelet (Level ) (Db) Kulwinder Singh Parmar, Rahmi Bhardwaj * Department of Mathematic, Univerity School of Baic and Applied Science, Guru Gobind Singh Indrapratha Univerity, Dwarka, Delhi,, India Abtract Statitical analyi of the water quality parameter COD (Chemical Oxygen Demand), BOD (Biochemical Oxygen Demand), DO (Diolved Oxygen), WT (Water Temperature), AMM (Free Ammonia), TKN (Total Kjeldahl Nitrogen), TC (Total Coliform), FC (Fecal Coliform) and ph (Potential of Hydrogen) monitored at Hathni Kund Dam (Haryana) Yamuna River in India have been tudied. It ha been oberved that water quality parameter have poitive correlation between COD-BOD; AMM-TKN; WT-pH; TC-FC; and negatively correlation between COD-DO; BOD-DO; TKN-FC; DO-WT. Dicrete wavelet analye of water quality parameter uing Daubechie wavelet at level have been calculated. It ha been oberved that the value of ignal data at five different level for AMM, BOD, COD, DO, FC, ph, TC, TKN, WT varie between - to, - to, - to, - to, to, - to, - to, to, - to repectively. Keyword Wavelet Analyi, Water Pollutant, Statitical Analyi, Daubechie Wavelet. Introduction Water i the baic requirement for life on earth. Many human activitie pollute the river water. Urbanization, indutrialization and globalization increaed pollution level in river water. Yu, B. et al. () [9] dicued the unteady evolution of NH 3 -N in the upper and middle reache of Minjiang River through multi-cale analyi. Zainuddin, Z. and Pauline, O. () [] decribed the predictive capability of Wavelet Neural Network (WNN). He, Li et al. (8) [] tudied wavelet-baed multireolution analyi technique (WMAT) for reducing noie induced by complex uncertainty. Hanbaya, D. et al. () [] tudied witch circuit model baed on wavelet decompoition and neural network. Kumar N. and Sinha D.K. () [] tudied tatitical regreion analyi of underground drinking water. Vaili Z. et al. () [8] tudied the time erie analyi uing tatitical method for monthly value of water quality parameter and the dicharge. Can, Z. et al. () [] analyzed the characteritic of gravity wave (GW) and eaonal variation of atmopheric wave over Itanbul uing wavelet technique. Zhang et al. (8) [] explained complex ytem dynamic (SD) model for water reource. Clonda, D. et al () [3] dicued ymmetric olution uing complex Daubechie wavelet. Bhardwaj et al. () [] calculated water quality index (WQI) for water quality parameter including cation, anion beide Diolved Oxide (DO), * Correponding author: rahmib@gmail.com (Rahmi Bhardwaj) Publihed online at Copyright Scientific & Academic Publihing. All Right Reerved Biochemical Oxygen Demand (BOD), Total Diolved Solid (TDS), Potential of Hydrogen (ph) and conductivity at the Hathni Kund Dam (Haryana, India). Thi paper deal with Statitical and Wavelet Analyi uing Daubechie Wavelet at level (Db ) of water quality parameter.. Statitical Analyi of Water Quality Parameter The monthly average value of lat year of water quality parameter COD (Chemical Oxygen Demand), BOD (Biochemical Oxygen Demand), DO (Diolved Oxygen), WT (Water Temperature), AMM (Free Ammonia), TKN (Total Kjeldahl Nitrogen), TC (Total Coliform), FC (Fecal Coliform) and ph (Potential of Hydrogen) oberved by Central Pollution Control Board (CPCB) at Hathni Kund Dam (Haryana) of Yamuna river (India) have been conidered for tudy. In Statitical analyi mean, median, mode, minimum, maximum, range, tandard deviation, kurtoi, kewne and coefficient of variation have been tudied. Skewne give the ymmetry of data and coefficient of variation dicribe the relative meaure of ample. Kurtoi (k) refer the degree of flatne or peakedne and it alo indicate impulivene of the ignal. It defined a ( ) ( ) k = σ x x f x dx () f x probability denity function of the intaneou xt at time t. x i a mean value and σ i the xt. The tatitical analyi of each water quality parameter where ( ) amplitude ( ) tandard deviation of ( )

2 8 Kulwinder Singh Parmar et al.: Analyi of Water Parameter Uing Daubechie Wavelet (Level ) (Db) ph, COD, BOD, AMM, TKN, DO, WT, TC and FC have been dicued below a given in Table. ph: Average, poitional average and mode value of ph i.,. and.. Thee value are cloe to. thu data exhibit normal behavior. Standard deviation (SD) i., kewne approximate to thu ph i ymmetrical and value are very cloe to each other. Curve i platykurtic a Kurtoi i le than 3. COD: Mean, median and mode value i.,. and. repectively thu curve i not normal. Standard deviation value i high (.938) thu value of COD are not cloe to each other. It i kewed (.3) and curve i leptokurtic becaue Kurtoi i more than 3. BOD: Mean and median value i approximately equal but mode value i different o curve i not normal. Standard deviation value ugget that data i pread out and curve i leptokurtic. AMM: Average, median and mode value i approximately equal thu data exhibit normal behavior. Standard deviation (.89) ugget that data i cloe to each other. Curve i platykurtic. TKN: Mean and median value i approximately equal. Standard deviation (.83) ugget that ample data i cloe to each other. Skewne value i approximately thu curve i ymmetrical and platykurtic. DO: Average, median and mode value i equal thu data behave normally. Standard deviation value i.3 curve i ymmetric and platykurtic. WT: Mean, median and mode value i approximate to thu data exhibit normal characteritic. Curve i kewed and platykurtic. Table. Statitical Analyi of Yamuna River at Hathni Kund Dam TC: Average, median and mode value i different. Standard deviation value explain that ample data i pread. Curve i leptokurtic. FC: Average, median and mode value i different. Standard deviation value explain that ample data i pread. Curve i leptokurtic. Curve i neither ymmetrical nor kewed. 3. Correlation Coefficient between Water Quality Parameter The correlation coefficient i defined a r xy i i nxy n xy i i x i y i xy = ( n = () ) δ x δ y n x i ( x i) n y i ( y i) where x and y are the ample mean of X and Y, and δ x and δ y are the ample tandard deviation of X and Y. Table-, give the value of correlation coefficient between pair of water quality parameter. It ha been oberved that COD i poitively correlated with BOD and negatively correlated with DO. Poitive correlation mean peritent behavior with the variable. BOD i negatively correlated with DO. AMM i poitively correlated with TKN. TKN i negatively correlated with TC. DO i negatively correlated with WT.WT i poitively correlated with ph and TC i poitive correlated with FC. Figure, plot the graphical repreentation of correlation coefficient of water quality parameter. Parameter ph COD BOD AMM TKN DO WT TC FC Mean ,,88. 8,. Median ,.,. Mode.. 9. Minimum Maximum ,3,,.,9,. Range ,9,99,9.,9,. SD Kurtoi Skewne Coeff. Of variation

3 American Journal of Mathematic and Statitic, (3): -3 9 Table. Correlation between water quality parameter at Hathni Kund (Haryana) Correlation PH COD BOD AMM TKN DO WT TC FC PH Pearon Correlation * Sig. (-tailed) N COD Pearon Correlation ** **...3 Sig. (-tailed) N BOD Pearon Correlation..38 ** * Sig. (-tailed) N AMM Pearon Correlation ** * Sig. (-tailed) N TKN Pearon Correlation ** Sig. (-tailed) N DO Pearon Correlation ** -.88 * ** Sig. (-tailed) N WT Pearon Correlation. *...9 *. -.9 ** -.3. Sig. (-tailed) N TC Pearon Correlation Sig. (-tailed) N FC Pearon Correlation Sig. (-tailed) N *. Correlation i ignificant at the. level (-tailed). **. Correlation i ignificant at the. level (-tailed). Correlation of ph with other parameter Correlation of BOD Correlation of COD Correlation of AMM

4 Kulwinder Singh Parmar et al.: Analyi of Water Parameter Uing Daubechie Wavelet (Level ) (Db) Correlation of TKN Correlation of FC Correlation of DO Correlation of WT Correlation of TC Figure. Pearon correlation coefficient of (a) ph (b) COD (c) BOD (d) AMM (e) TKN (f) DO (g) WT (h) TC and (i) FC.. Dicrete Wavelet Analyi of Water Quality Parameter A wavelet i a function ψ L ( ) condition ( ) which atifie the ψ ω Cψ dω < (3) ω where ψ ( ω ) i the Fourier tranform of ψ ( t) It may be oberved that the wavelet tranform i a prim which exhibit propertie of ignal uch a point of abrupt change, eaonality or periodicity. The wavelet tranform i a function of a and b where a = the cale of frequency b = patial poition (tranlation) or time The plane defined by the variable (a, b) i called the cale-pace or time frequency plane. A continuou repreentation of a function of two continuou parameter a, b can be converted into a dicrete one by auming that a and b take only integral value. ( ) t ψ t = a ψ, where a ab, > () a Tψ f( ab, ) i called the Wavelet Tranform of f ( t) and (, ) t Tψ f a b = a f ( t) ψ dt = f, ψ a ab, = inner product or dot product of f andψ ab, If ψ L ( ), then ψ ( t ab, ) L ( ) for all a, b. t ψab, ( t) = a ψ dt = ψ ( x) dx = ψ a () The Fourier tranform i given by iωt t iωt ψ ( ) ab, ω = a e ψ dt = a e ψ ( aω) a () One dimenional dicrete wavelet analyi of monthly average value for lat ten year of water quality parameter

5 American Journal of Mathematic and Statitic, (3): -3 uch a ph, BOD, COD, DO, AMM, TKN, WT, TC and FC for Yamuna river at Hathni Kund Dam, Haryana uing ten year value. Daubechie wavelet at level (Db ) contain even part, a, d, d,, and d. The firt part repreent the ignal or raw data and the econd part a correpond to the amplitude of the ignal. The lat part d, d,, and d repreent detail of the ignal or raw data at five different level. Decompoition at level : = a + d + d + d3 + d + d a d - d - Decompoition at level : = a + d + d + d3 + d + d...3. a... d d d d Figure (d). D Dicrete wavelet for DO d -. x Decompoition at level : = a + d + d + d3 + d + d. d x Figure (a). D Dicrete wavelet for AMM a x Decompoition at level : = a + d + d + d3 + d + d. d 3 x..3 a... x d x d d d - x d d Figure (e). D Dicrete wavelet for FC Figure (b). D Dicrete wavelet for BOD 9 8 Decompoition at level : = a + d + d + d3 + d + d. Decompoition at level : = a + d + d + d3 + d + d. a d a.... d -.. d d d -. - d d Figure (c). D Dicrete wavelet for COD Figure (f). D Dicrete wavelet for ph

6 Kulwinder Singh Parmar et al.: Analyi of Water Parameter Uing Daubechie Wavelet (Level ) (Db) a d d d a d d d. a.8.. d d d - - x 3 x x - x x x - x Decompoition at level : = a + d + d + d3 + d + d Figure (g). D Dicrete wavelet for TC Decompoition at level : = a + d + d + d3 + d + d Figure (h). D Dicrete wavelet for TKN Decompoition at level : = a + d + d + d3 + d + d Figure (i). D Dicrete wavelet for WT Figure, give the detail of D Daubechie Wavelet analyi at level (Db ) for each water quality parameter. It ha been oberved that: AMM: The firt part of the figure (a) how that maximum value of AMM i.33 and the correponding amplitude (a ) varie from. to.3. The value of d,,, d and d vary from-. to., -. to., -. to., -. to. and - to repectively. BOD: Figure (b) explain the BOD parameter ignal and maximum value i and amplitude (a ) of thi ignal varie from. to.. The other value of d,,, d and d varie from -. to., -. to., - to., - to and - to repectively. COD: Figure (c) explain the COD parameter ignal and maximum value i 3 and amplitude (a ) varie from. to 9.. The other value of d,,, d and d varie from - to, - to, to, - to and - to repectively. DO: Figure (d) decribe the DO parameter ignal and maximum value i 3 and amplitude (a ) varie from 9. to 9.9. The other value of d,,, d and d vary from - to, - to, - to, - to and - to repectively. FC: Figure (e) explain the FC parameter ignal and maximum value i and amplitude (a ) varie from to. The other value of d,,, d and d vary from to, to, - to, - to and to repectively. ph: Figure (f) depict the ph parameter ignal and maximum value i 9 and amplitude (a ) varie from. to.8. The other value of d,,, d and d varie from -. to., -. to., -. to., -. to. and - to repectively. TC: Firt part of the Figure (g) explain the TC parameter ignal and maximum value a 3 and am- plitude (a ) varie from to. The other value of d,,, d and d vary from - to, to, to, - to and - to repectively. TKN: Figure (h) explain the TKN parameter ignal and give maximum value i. and amplitude (a ) varie from. to.. The other value of d,,, d and d varie from -. to., - to, -. to., - to and to repectively. WT: Figure (i) explain the WT parameter ignal and maximum value i 9 and amplitude (a ) varie from. to.. The other value of d,,, d and d vary from - to, to, to, - to and - to repectively.. Concluion Statitical and wavelet analyi of water quality parameter monitored at the Hathni Kund Dam (Haryana) of Yamuna River (India) have been dicued. It ha been oberved that curve i platykurtic for ph, AMM, TKN, DO, WT; leptokurtic for COD, BOD, TC, FC and normal for ph, AMM, DO, WT. There i poitive correlation between COD BOD, AMM TKN, WT ph, TC FC and negative correlation between COD DO, BOD-DO, TKN FC, DO WT. -D Dicrete Daubechie Wavelet analyi explain that the parameter AMM, BOD, COD, DO, FC, ph, TC, TKN and WT have the maximum value.33,., 3, 3,

7 American Journal of Mathematic and Statitic, (3): -3 3, 9., 3,. an and amplitude (a ) varie between. to.3,. to.,. to 9., 9. to 9.9, to,. to.8, to,. to. and. to. repectively. The value of d,,, d and d range between - to for AMM, ph; - to for BOD, DO, TC; to for FC, TKN; - to for WT and - to for COD. It ha been concluded that water quality parameter cro the precribed limit of WHO/EPA. ACKNOWLEDGEMENTS Author are thankful to Guru Gobind Singh Indrapratha Univerity for providing reearch facilitie and financial upport. Author alo thankful to Central Pollution Control Board (CPCB) for providing data for reearch work. REFERENCES [] Bhardwaj, R., Parmar, K.S., Chuhg, P., Minha, P.and Sahota, H.S. () Seaonal variation of phyico- chemical parameter and water quality indexing of Harike Lake Indian j.env.prot, 3(), 8-8. [] Can, Z.; Alan, Z., Oguz, O. and Siddiqi, A.H. () Wavelet Tranform of Metrological Parameter and Gravity Wave Annale Geophyicae, 3, 9-3. [3] Clonda, D., Lina, J. and Goulard, B. () Complex Daubechie wavelet: propertie And tatitical image modeling Signal Proceing, 8 (), -3. [] Hanbaya, D., Turkoglua, I., and Demirb, Y. () Modeling witched circuit baed on wavelet decompoition and neural network Journal of the Franklin Intitute, 3(3), -. [] He, L., Huang, G., Zeng, G. and Lu, H. (8) Wavelet-baed multireolution analyi for data cleaning and it application to water quality management ytem Expert Sytem with Application, 3 (3), 3-3. [] Kumar, N. and Sinha, D.K. () Drinking water quality management through Correlation tudie among variou phyico- chemical parameter: A cae tudy I.J.Env.Sci, (), 39. [] Shukla, J.B., Mira, A.K. and Chandra, P. (8) Mathematical Modeling and analyi of the diolved oxygen in eutrophied water bodie affected by organic pollutant Nonlinear Analyi: Real world Application, 9, 8-8. [8] Vaili, Z., Papamichail, D.M. and Mitiou () Statitical and trend analyi of water quality and quantity data for the Strymon River in Greece Hydrology and Earth Sytem Science, (), 9-9. [9] Yu, B., Huang, C.M., Liu, Z., Zhang, B. and Qin, F. () Wavelet Analyi on NH 3 - N Pollution Index Change of the Middle-Upper Minjiang River during Lat Year International Society for Environmental Information Science Annual Conference (ISEIS) Procedia Environmental Science,, 9-. [] Zainuddin, Z. and Pauline, O. () Modified wavelet neural network in function approximation and it application in prediction of time-erie pollution data Applied Soft Computing, (8), 8 8. [] Zhang, X.H., Zhang, H.W., Chen, B. and Zhao, X.H (8) Water reource planning baed on complex ytem dynamic: A cae tudy of Tianjin city Commun. Nonlinear Sci. Numer. Simul., 3(),