**5. Concentration measurement estimation results**

The performance of the FCM based fuzzy rule based model is evaluated based on performance indices as described in performance evaluation criteria. These include root mean square error (RMSE), correlation coefficient (R) between the actual and estimated monthly average concentration measurement values of atrazine herbicides, standard error of estimate (SEE) and MENash. The performance evaluation results of the fuzzy rule based model with four fuzzy variables obtained using FCM, represented as Fuzzy\_4\_FCM, is also compared with that of the fuzzy rule based models with 3, 5, 7 linguistic variables for both of the input 1 and input 3. The performance of the Fuzzy\_4\_FCM model is also compared with solution results of an artificial neural network (ANN) based model using back propagation algorithm (Rumelhart et al. 1986) as represented by ANN\_M in Table 3.



It can be noted from the Table 3 that the error statistics are better for Fuzzy\_4M\_FCM model than those of Fuzzy\_3M, Fuzzy\_5M and ANN\_M model in both the training and testing in prediction in atrazine concentration measurement values. Its performance is even better than Fuzzy\_7M model in training. Model efficiency (MENash) in training is 94.3 percent whereas it is 91.5 percent for Fuzzy\_7M model. Similarly, RMSE, R, and SSE values are also comparable. In testing, results are also comparable though error statistics for Fuzzy\_7M model is slightly better than Fuzzy\_4\_FCM. Thus, the FCM optimized fuzzy membership functions partitions in Fuzzy\_4\_FCM model are performing comparable to almost double the fuzzy partitions without FCM in Fuzzy\_7M model. Figure 2 shows better RMSE value by Fuzzy\_4\_FCM model in comparison to other models.

It can also be noted from Table 3 that performances of fuzzy rule based model is better than those obtained using an ANN model with 2 inputs (atrazine application rate and weighted percentage area), 12 outputs (average monthly concentration measurements), and 11 hidden nodes (selected on the basis of experimentation) represented by ANN\_M model. The poor performance by ANN\_M model may be due to inadequate training patterns for experimentation, as the total number of free parameters become more than the number of training patterns even for 1 hidden node in hidden layer.

Prediction of Herbicides Concentration in Streams 241

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months of the Year 1999

Fig. 4. Comparison of observed and Fuzzy\_4\_FCM predicted average monthly atrazine

months values including peak value does not mach well as shown in Figure 6.

R2

Fig. 5. Scatter plot of observed and Fuzzy\_4\_FCM Model predicted average monthly

= 0.9524

1:1 Line Fuzzy\_4\_FCM

Linear (1:1 Line) Linear (Fuzzy\_4\_FCM)

0123456 Actual Attrazine Concetration

Figure 5 represents scatter plot of observed and Fuzzy\_4\_FCM predicted values, and Figure 6 represents comparison of observed and Fuzzy\_4\_FCM predicted atrazine concentration values for the period 2000. Scatter plots between the observed and Fuzzy\_4\_FCM predicted average atrazine concentration measurement values in stream followed a 1:1 line with R2 value of 0.95. In this case though initial and final months values matches well, intermediate

Actual Fuzzy\_4\_FCM

0 0.5 1 1.5 2 2.5 3 3.5 4

atrazine concentration for the testing period year 2000.

Estimated Attrazine

Concentration

concentration for the testing period year 1999.

Average Attrazine

Concentration (µg/l)

Fig. 2. Performance comparison of models.

Scatter plots of average monthly observed and predicted atrazine concentration measurement in the stream for model Fuzzy\_4\_FCM are plotted for the testing period 1999, 2000, and 2001. Comparison of actual and model estimated values are also presented for average monthly variations of atrazine concentration in the stream during the testing period, 1999-2001. Figure 3 represents scatter plot, and Figure 4 represents comparison of actual and Fuzzy\_4\_Model estimated values for the period 1999. Scatter plots between the observed and Fuzzy\_4\_FCM predicted average atrazine concentration measurement values in stream followed a 1:1 line except for a few cases of high magnitudes. The high values of coefficient of determination, R2 (0.933), indicate that there is a good match between the observed and model predicted atrazine concentration. Figure 4 shows a comparison of observed and, Fuzzy\_4\_FCM model predicted average monthly atrazine concentration measurement values in the stream. The observed and Fuzzy\_4\_FCM predicted values match well except for the occurrence of peak value.

Fig. 3. Scatter plot of observed and Fuzzy\_4\_FCM Model predicted average monthly atrazine concentration for the testing period year 1999.

Fuzzy\_3M Fuzzy\_5M Fuzzy\_7M ANN\_M Fuzzy\_4\_FCM

1990 2000 2001 Years

Scatter plots of average monthly observed and predicted atrazine concentration measurement in the stream for model Fuzzy\_4\_FCM are plotted for the testing period 1999, 2000, and 2001. Comparison of actual and model estimated values are also presented for average monthly variations of atrazine concentration in the stream during the testing period, 1999-2001. Figure 3 represents scatter plot, and Figure 4 represents comparison of actual and Fuzzy\_4\_Model estimated values for the period 1999. Scatter plots between the observed and Fuzzy\_4\_FCM predicted average atrazine concentration measurement values in stream followed a 1:1 line except for a few cases of high magnitudes. The high values of coefficient of determination, R2 (0.933), indicate that there is a good match between the observed and model predicted atrazine concentration. Figure 4 shows a comparison of observed and, Fuzzy\_4\_FCM model predicted average monthly atrazine concentration measurement values in the stream. The observed and Fuzzy\_4\_FCM predicted values match

> R2 = 0.933

1:1 Line Fuzzy\_4\_FCM

Linear (1:1 Line) Linear (Fuzzy\_4\_FCM)

0 0.5 1 1.5 2 2.5 3 3.5 Actual Attrazine Concentration

Fig. 3. Scatter plot of observed and Fuzzy\_4\_FCM Model predicted average monthly

0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600

Fig. 2. Performance comparison of models.

well except for the occurrence of peak value.

0

atrazine concentration for the testing period year 1999.

1 2

3

Estimated Attrazine

Concentration

4

RMSE

Fig. 4. Comparison of observed and Fuzzy\_4\_FCM predicted average monthly atrazine concentration for the testing period year 1999.

Figure 5 represents scatter plot of observed and Fuzzy\_4\_FCM predicted values, and Figure 6 represents comparison of observed and Fuzzy\_4\_FCM predicted atrazine concentration values for the period 2000. Scatter plots between the observed and Fuzzy\_4\_FCM predicted average atrazine concentration measurement values in stream followed a 1:1 line with R2 value of 0.95. In this case though initial and final months values matches well, intermediate months values including peak value does not mach well as shown in Figure 6.

Fig. 5. Scatter plot of observed and Fuzzy\_4\_FCM Model predicted average monthly atrazine concentration for the testing period year 2000.

Prediction of Herbicides Concentration in Streams 243

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months of the Year 2001

Fig. 8. Comparison of observed and Fuzzy\_4\_FCM model predicted average monthly

performance of the methodology in different evaluation periods, under or over prediction of peak values, fuzzy rule based model control parameters (shape, total number of fuzzy centers, overlaps etc. of membership functions; fuzzy set operations i.e, defuzzification

The performance of fuzzy rule based model with FCM is better than those without FCM model with even more number of fuzzy partitions. This is inferred by comparison of performances of Fuzzy\_4\_FCM model with Fuzzy\_3M, Fuzzy\_5M, and Fuzzy\_7M models. In all the evaluation results obtained by Fuzzy\_4\_FCM model for the period 1999-2001, the R2 values from scatter plots, and MENash values obtained from observed and model predicted values are high ( around 0.9). This implies good match between the observed and model predicted values. The fuzzy rule with FCM model also performed better than the ANN based model. It establishes that the developed fuzzy rule based model with FCM is potentially suitable for estimation of concentration measurement values with limited data availability. The performances of the developed models are better in comparison to performance of regression models developed for the Mississippi River Systems (Battaglin and Goolsby, 1997). Their study show that multiple linear regression models estimate the concentration of selected agricultural chemicals with maximum R-squared value is 0.514, and in the case of atrazine, R-squared value is 0.312. In this study, almost all the developed models have R-squared value greater than 0.55. However, this comparison is limited as the White River basin considered in this study is only a part of (one of 10 basins) of Mississippi

The estimation results obtained using fuzzy rule based models are encouraging but not conclusive. In almost all the evaluations, though initial months and final months concentration measurement values matches well, the intermediate values including the peak values are either over predicted or under predicted except for the year 2001 where peak predicted value matched well with the observed value. As the intermediate months, from April to July observes most of the changes in atrazine observed concentration measurement values, the same dynamics are exactly not reflected in model predictions. Thus, though the FCM model works better than ANN model in case of limited data availability, its

Actual Fuzzy\_4\_FCM

0.000 0.500 1.000 1.500 2.000 2.500 3.000

atrazine concentration for the testing period year 2001.

River Systems considered by them (Battaglin and Goolsby, 1997).

methods etc.) needs to be investigated further.

Average Attrazine

Concentration (µg/l)

Fig. 6. Comparison of observed and Fuzzy\_4\_FCM predicted average monthly atrazine concentration for the testing period year 2000.

Figure 7 represents scatter plot of observed and Fuzzy\_4\_FCM predicted values, and Figure 8 represents comparison of observed and Fuzzy\_4\_FCM model predicted atrazine concentration values for the period 2001. Scatter plots between the observed and Fuzzy\_4\_FCM predicted average atrazine concentration measurement values in stream followed a 1:1 line with high value R2 (0.93).

Fig. 7. Scatter plot of observed and Fuzzy\_4\_FCM Model predicted average monthly atrazine concentration for the testing period year 2001.

#### **6. Discussion of results**

The performance evaluation results presented in this study establish the potential applicability of the developed methodology in estimation of monthly atrazine concentration measurement values using fuzzy rule based models with FCM. However, the comparative

Actual Fuzzy\_4\_FCM

1 2 3 4 5 6 7 8 9 10 11 12 Months of the Year 2000

R2

Linear (1:1 Line) Linear (Fuzzy\_4\_FCM)

0.000 0.500 1.000 1.500 2.000 2.500 3.000 **Actual Attrazine Concentration**

Fig. 7. Scatter plot of observed and Fuzzy\_4\_FCM Model predicted average monthly

The performance evaluation results presented in this study establish the potential applicability of the developed methodology in estimation of monthly atrazine concentration measurement values using fuzzy rule based models with FCM. However, the comparative

= 0.9269

Fig. 6. Comparison of observed and Fuzzy\_4\_FCM predicted average monthly atrazine

Figure 7 represents scatter plot of observed and Fuzzy\_4\_FCM predicted values, and Figure 8 represents comparison of observed and Fuzzy\_4\_FCM model predicted atrazine concentration values for the period 2001. Scatter plots between the observed and Fuzzy\_4\_FCM predicted average atrazine concentration measurement values in stream

1:1 Line Fuzzy\_4\_FCM

concentration for the testing period year 2000.

followed a 1:1 line with high value R2 (0.93).

0.000 0.500 1.000 1.500 2.000 2.500 3.000

atrazine concentration for the testing period year 2001.

**Estimated Attrazine** 

**Concentration**

**6. Discussion of results** 

Average Attragine

Concentration (µg/l)

Fig. 8. Comparison of observed and Fuzzy\_4\_FCM model predicted average monthly atrazine concentration for the testing period year 2001.

performance of the methodology in different evaluation periods, under or over prediction of peak values, fuzzy rule based model control parameters (shape, total number of fuzzy centers, overlaps etc. of membership functions; fuzzy set operations i.e, defuzzification methods etc.) needs to be investigated further.

The performance of fuzzy rule based model with FCM is better than those without FCM model with even more number of fuzzy partitions. This is inferred by comparison of performances of Fuzzy\_4\_FCM model with Fuzzy\_3M, Fuzzy\_5M, and Fuzzy\_7M models. In all the evaluation results obtained by Fuzzy\_4\_FCM model for the period 1999-2001, the R2 values from scatter plots, and MENash values obtained from observed and model predicted values are high ( around 0.9). This implies good match between the observed and model predicted values. The fuzzy rule with FCM model also performed better than the ANN based model. It establishes that the developed fuzzy rule based model with FCM is potentially suitable for estimation of concentration measurement values with limited data availability. The performances of the developed models are better in comparison to performance of regression models developed for the Mississippi River Systems (Battaglin and Goolsby, 1997). Their study show that multiple linear regression models estimate the concentration of selected agricultural chemicals with maximum R-squared value is 0.514, and in the case of atrazine, R-squared value is 0.312. In this study, almost all the developed models have R-squared value greater than 0.55. However, this comparison is limited as the White River basin considered in this study is only a part of (one of 10 basins) of Mississippi River Systems considered by them (Battaglin and Goolsby, 1997).

The estimation results obtained using fuzzy rule based models are encouraging but not conclusive. In almost all the evaluations, though initial months and final months concentration measurement values matches well, the intermediate values including the peak values are either over predicted or under predicted except for the year 2001 where peak predicted value matched well with the observed value. As the intermediate months, from April to July observes most of the changes in atrazine observed concentration measurement values, the same dynamics are exactly not reflected in model predictions. Thus, though the FCM model works better than ANN model in case of limited data availability, its

Prediction of Herbicides Concentration in Streams 245

Capel Paul D., Larson Steven J. (2001) Effect of Scale on the Behavior of Atrazine in Surface

Charbeneau R., Barrett M. (1998) Evaluation of methods for estimating storm water

Crawfard C.G. (2001) Factors Affecting Pesticide Occurrence And Transport In A Large Mid-Western River Basin. *Journal of American Water Res. Asstn.* 37(1): 1-15, 2001. Crawford, C.G. (1995) Occurrence of pesticides in the White River, Indiana, 1991-95: U*.S.* 

Coupe R. H., Goolsby D. A., Iverson J. L., Zaugg S.D., Markovchick D. J. (1995) Pesticide,

Dadone P, VanLandingham H.F. (2000) On the differentiability of fuzzy logic systems.

D'Arcy B.J., Ellis J.B., Ferrier R.C., Jenkins A., Dils R. (eds.) (2000) Diffuse pollution impacts,

Dunn J. C. (1973) A Fuzzy Relative of the ISODATA process and its use in detecting

Goolsby D. A., Battaglin, W. A. (1993) Occurrence, distribution, and transport of agricultural

Goolsby D. A., Battaglin, W. A. (1995) Occurrence, and distribution of pesticides in rivers of

Guillaume S, Charnomordic B. (2004) Generating an interpretable family of fuzzy partitions

Jha, R., Ojha, C.S.P, Bhatia, K.K.S., 2005. Estimating nutrient outflow from agricultural

Khrisnapuram R. (1998) Membership function elicitation and learning. In: Ruspini E.H.,

Larson Steven J. and Gilliom Robert J. (2001) Regression Models For Estimating Herbicides

Mahabir C, Hicks, F.E., Fayek A.R. (2003) Application of fuzzy logic to forecast seasonal

Mahar, P.S., and Datta, B. (2000) Identification of pollution sources in transient groundwater

Nash J. E., and Sutcliffe, J. V. (1970) River flow forecasting through conceptual models. Part

Novotny V., Water Quality (2nd edition) (2003), *Diffuse Pollution & Watershed Management.*

*Institution of Environmental Management(CIWEM), Lavenham Press.* 

compact well-separated clusters*. Journal of Cybernetics* 3: 32-57

from data*. IEEE transactions on Fuzzy Systems,* 12 (3): 324-335.

Physics Publishing, Dirac House, Temple Bath, Bristol.

system. *Water Resource Management* 14(6): 209 - 227.

John Wiley and Sons, New York. ISBN 0-471-39633-8.

1-A: Discussion principles. *J. Hydrol.* 10: 282–290

Nutrient, Streamflow and Physical Property Data for the Mississippi River, and Major Tributaries, April 1991- September, 1992. *U.S. Geol. Surv. Open-File* Rep. 93-

*Proceedings of IEEE Conference on Systems, Man and Cybernetics*, Nashville, TN, 2703-

the environmental and economic impacts of diffuse pollution in the UK, *Chartered* 

chemicals in surface waters of the midwestern United States, In: Goolsby D. A., Boyer L.L, Mallard G.E. (Eds.), Selected papers on agricultural chemicals in Water Resources Midcontinental United States. *U S Geological Survey Open-*File Rep. 93-

the midwestern United States, In: Leng, M.L., Leovey, E.M.K., Zubkoff, P.L.(Eds.), *Agrochemical Environmental Fate: State of the Art.* CRC Press Inc., Boca Raton, FL:

watersheds to the river Kali in India. *Journal of Environmental Engineering*, ASCE,

Bonissone P.P., Pedrryez W. (eds.). *Handbook of Fuzzy Computation*, Institute of

Concentrations In U.S. Streams From Watershed Characteristics, *Journal of American* 

pollutant loads, *Water Environment Research:* 70(7), 1295-1302.

Waters. *Envron. Sci. Technol.* 35(4): 648-657, 2001.

*Geological Survey Fact Sheet No. 233-95.*

657.

2708.

418: 1-24

159-173.

131(12), 1706–1715.

*Water Res. Asstn*. 3(5): 1349-1367.

runoff. *Hydrol. Process.* 17: 3749-3762.

performance is also affected due to limited data sets. In the present study, the inputs were assigned with triangular shape. Further improvement in the performance of the methodology may be possible with more extensive evaluations of membership functions shape, number of data centers for membership functions for each variables, and overlap between two membership functions. Present methodology utilized centroid method for defuzzification. Performance of other defuzzification method also need to be investigated. The error in prediction of peak values shows the limitation of the methodology. However, these results show potential applicability of the proposed methodology. The main advantage of the developed methodology is incorporate some prior knowledge into the model frame work, and its ability to perform in case of limited availability of data than other methods such as ANN.
