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Degrees of fitness (in terms of R2 and RMSE) of modeling calculated using the parameters obtained from the regression equations in Table 6 are presented in Table 7. R2s and RMSEs for the nth-order and limited nth-order models tend to decrease and increase, respectively, as the order n of the models is increased. Both R2 and RMSE for the five generic models (from the nth-order model to the combined ‘n + n’ model) are generally superior to the nine existing models. These findings indicate that the introduction of additional calibration parameters and relaxation limitations to chlorine decay order in model structure improve the predictability of chlorine decay behavior substantially even in modeling considering turbulence intensity for parameter evaluation. Chlorine decay models with low order (n ≤ 1) showed good performance in terms of predictability and parsimony of model parameter than those for high order models.

Table 7

Validation of power regression equations

It
274.90
682.72
1,727.66
4,379.45
9,712.18
TitleR2RMSER2RMSER2RMSER2RMSER2RMSE
1st order 0.99 0.055 0.99 0.056 0.98 0.076 0.99 0.059 0.97 0.101 
2nd order 0.92 0.141 0.93 0.136 0.89 0.181 0.90 0.171 0.87 0.204 
3rd order 0.83 0.212 0.83 0.215 0.78 0.253 0.79 0.249 0.77 0.274 
4th order 0.72 0.269 0.73 0.271 0.68 0.304 0.69 0.303 0.68 0.324 
Limited 1st order 0.99 0.059 0.99 0.055 0.98 0.079 0.99 0.062 0.97 0.103 
Limited 2nd order 0.92 0.143 0.93 0.141 0.88 0.184 0.90 0.175 0.87 0.207 
Limited 3rd order 0.92 0.148 0.87 0.186 0.85 0.206 0.84 0.218 0.86 0.216 
Limited 4th order 0.72 0.269 0.73 0.275 0.67 0.307 0.68 0.306 0.67 0.328 
Parallel 1st order 0.99 0.056 0.99 0.055 0.98 0.076 0.99 0.059 0.97 0.099 
nth order 0.99 0.050 0.98 0.066 0.99 0.044 1.00 0.026 0.99 0.056 
Limited nth order 0.99 0.049 0.98 0.071 0.99 0.042 1.00 0.026 0.99 0.054 
Combined ‘1 + 1’ 0.99 0.051 0.98 0.067 0.98 0.077 0.98 0.066 0.97 0.102 
Combined ‘1 + n’ 0.99 0.051 0.95 0.117 0.97 0.090 0.99 0.062 0.97 0.102 
Combined ‘n + n’ 1.00 0.030 0.97 0.084 0.99 0.048 1.00 0.032 0.98 0.085 
It
274.90
682.72
1,727.66
4,379.45
9,712.18
TitleR2RMSER2RMSER2RMSER2RMSER2RMSE
1st order 0.99 0.055 0.99 0.056 0.98 0.076 0.99 0.059 0.97 0.101 
2nd order 0.92 0.141 0.93 0.136 0.89 0.181 0.90 0.171 0.87 0.204 
3rd order 0.83 0.212 0.83 0.215 0.78 0.253 0.79 0.249 0.77 0.274 
4th order 0.72 0.269 0.73 0.271 0.68 0.304 0.69 0.303 0.68 0.324 
Limited 1st order 0.99 0.059 0.99 0.055 0.98 0.079 0.99 0.062 0.97 0.103 
Limited 2nd order 0.92 0.143 0.93 0.141 0.88 0.184 0.90 0.175 0.87 0.207 
Limited 3rd order 0.92 0.148 0.87 0.186 0.85 0.206 0.84 0.218 0.86 0.216 
Limited 4th order 0.72 0.269 0.73 0.275 0.67 0.307 0.68 0.306 0.67 0.328 
Parallel 1st order 0.99 0.056 0.99 0.055 0.98 0.076 0.99 0.059 0.97 0.099 
nth order 0.99 0.050 0.98 0.066 0.99 0.044 1.00 0.026 0.99 0.056 
Limited nth order 0.99 0.049 0.98 0.071 0.99 0.042 1.00 0.026 0.99 0.054 
Combined ‘1 + 1’ 0.99 0.051 0.98 0.067 0.98 0.077 0.98 0.066 0.97 0.102 
Combined ‘1 + n’ 0.99 0.051 0.95 0.117 0.97 0.090 0.99 0.062 0.97 0.102 
Combined ‘n + n’ 1.00 0.030 0.97 0.084 0.99 0.048 1.00 0.032 0.98 0.085 

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