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.
Validation of power regression equations
It . | 274.90 . | 682.72 . | 1,727.66 . | 4,379.45 . | 9,712.18 . | |||||
---|---|---|---|---|---|---|---|---|---|---|
Title . | R2 . | RMSE . | R2 . | RMSE . | R2 . | RMSE . | R2 . | RMSE . | R2 . | RMSE . |
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 . | |||||
---|---|---|---|---|---|---|---|---|---|---|
Title . | R2 . | RMSE . | R2 . | RMSE . | R2 . | RMSE . | R2 . | RMSE . | R2 . | RMSE . |
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 |