APPENDIX A Watershed Delineation and Stream Network Defined from WMS
Figure A.1. Subbasins Delineation and Stream Network for Goodwin Creek Watershed
APPENDIX B Summary Statistics of Monthly Peak Discharge Data (cfs)
Table B.1 Summary Statistics for Subbasin 1 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 799.1 683.5 611.6 231 2.2E+8.96.56.77 2 185.6 922. 146.9 3739 1.8E+9 1.6 1.92.96 3 1227.9 192. 8.9 2967 4.6E+8.89 -.5.65 4 142.9 982. 83.8 3596 9.3E+8 1.62 4.43.8 5 1129.1 466.5 168.8 527 8.4E+9 1.77 1.83 1.49 6 646. 463.5 641.7 212 3.2E+8 1.21.43.99 7 583.9 179. 917.2 366 1.9E+9 2.53 6.91 1.57 8 465.2 12.5 675.5 2516 5.9E+8 1.9 3.99 1.45 9 441.2 16.5 99.6 3758 2.7E+9 2.81 7.83 2.25 1 327.5 13.5 619. 1954 4.6E+8 1.94 2.47 1.89 11 659.7 468.5 62.7 2146 2.4E+8 1.1.29.94 12 16. 77.5 92.1 3383 9.4E+8 1.21 1.34.87
Table B.2 Summary Statistics for Subbasin 2 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 674.9 589. 462. 1593 5.8E+7.59 -.54.68 2 893.6 74. 779.7 2695 6.4E+8 1.36 1.26.87 3 1155.7 989. 761. 2774 3.7E+8.84 -.25.66 4 889.6 813.5 587.2 192 3.1E+7.15-1.18.66 5 117. 441.5 152.9 4686 6.1E+9 1.79 2.2 1.48 6 647.2 451.5 666.3 2423 4.3E+8 1.45 1.77 1.3 7 557.4 196. 829.3 373 1.2E+9 2.18 4.65 1.49 8 436.4 115.5 68.8 2171 3.8E+8 1.67 2.64 1.4 9 43.9 18. 866.6 3194 1.7E+9 2.64 6.64 2.15 1 311.9 12. 592.5 1982 4.3E+8 2.5 3.24 1.9 11 638.7 416.5 625. 231 2.4E+8 1. -.7.98 12 971.3 717.5 928.5 3256 1.2E+9 1.45 1.76.96
Table B.3 Summary Statistics for Subbasin 3 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 426.6 383.5 33.6 1219 3.7E+7 1.2.54.77 2 6.6 393. 735.8 2925 9.4E+8 2.35 5.65 1.23 3 633.1 58. 46.2 147 5.8E+7.86.6.64 4 545.9 512.5 451.6 1975 1.7E+8 1.86 5.3.83 5 121.7 248. 1851.2 5695 1.2E+1 1.96 2.36 1.81 6 447.9 364. 433.1 1681 1.2E+8 1.42 2.6.97 7 38.3 16.5 721.5 27 9.9E+8 2.64 6.64 1.9 8 265.7 38.5 443.9 1739 2.1E+8 2.43 6.83 1.67 9 423.7 14.5 168. 439 4.2E+9 3.44 12.5 2.52 1 237.9 2. 489.7 1739 2.7E+8 2.3 4.8 2.6 11 353.4 243.5 317.2 151 2.4E+7.75 -.43.9 12 624.6 421.5 7.6 2832 7.6E+8 2.21 5.47 1.12
Table B.4 Summary Statistics for Subbasin 4 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 196.8 185.5 151.6 577 3.4E+6.96.77.77 2 262. 193.5 26.4 955 3.E+7 1.67 2.42.99 3 33.2 287.5 198.1 723 5.6E+6.72 -.51.6 4 273.7 264.5 21.1 829 8.3E+6 1.2 2.18.74 5 348.6 132.5 521.6 1691 2.6E+8 1.83 2.31 1.5 6 29.1 124.5 214. 689 1.2E+7 1.21.32 1.2 7 217.8 48.5 326.9 141 6.1E+7 1.74 1.95 1.5 8 18.3 47. 252. 793 2.3E+7 1.41.91 1.4 9 131.3.5 298.3 113 7.2E+7 2.69 6.98 2.27 1 86.6 2.5 165.1 531 8.9E+6 1.98 2.75 1.91 11 166.2 126.5 151.1 442 2.2E+6.65-1.2.91 12 256.1 218.5 29.2 686 7.3E+6.8 -.2.82
Table B.5 Summary Statistics for Subbasin 5 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 229.4 164. 192.6 686 7.2E+6 1.1.25.84 2 38. 236.5 339.8 1289 7.7E+7 1.95 3.64 1.1 3 393.8 353.5 259. 895 9.8E+6.57 -.69.66 4 346.4 328. 291.2 1264 4.5E+7 1.83 5.19.84 5 42.2 126.5 61.3 182 4.E+8 1.77 1.85 1.52 6 291. 26. 321.1 132 6.8E+7 2.5 5.6 1.1 7 184.1 85. 296.1 1176 6.8E+7 2.62 7.37 1.61 8 136.3 21.5 191.2 585 8.5E+6 1.22.19 1.4 9 16.7 7.5 346.1 14 1.3E+8 3.9 1.37 2.15 1 126.1 9.5 242.5 71 2.7E+7 1.89 2.4 1.92 11 243.7 149. 222.5 61 5.9E+6.54-1.42.91 12 318.4 233. 291.7 1 3.1E+7 1.23.89.92
Table B.6 Summary Statistics for Subbasin 6 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 84.1 71.5 69. 272 4.3E+5 1.3 1.94.82 2 111.1 73. 129.6 499 4.7E+6 2.17 4.45 1.17 3 14.4 17.5 96.4 316 6.3E+5.7 -.84.69 4 115.1 98.5 85.7 313 6.E+5.96.45.74 5 132.1 48. 196. 56 1.3E+7 1.67 1.35 1.48 6 121.2 71. 148.3 593 7.2E+6 2.21 5.62 1.22 7 64.4 18. 99.6 281 1.6E+6 1.6 1.6 1.55 8 42.9 4. 68.5 215 6.1E+5 1.89 2.86 1.6 9 78.2 4. 14.9 477 5.2E+6 1.86 2.79 1.8 1 38.7.5 77.5 276 1.1E+6 2.29 4.79 2. 11 73.4 5. 81.1 271 6.6E+5 1.24.63 1.11 12 13.7 73.5 98.4 336 1.1E+6 1.12.5.95
Table B.7 Summary Statistics for Subbasin 7 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 113.9 13.5 89.9 344 8.3E+5 1.14 1.32.79 2 143.4 12.5 143.7 494 4.6E+6 1.54 1.68 1. 3 198.7 165. 117.3 43 1.E+6.62 -.8.59 4 157.3 163. 123.2 516 2.4E+6 1.3 3.17.78 5 253.7 76. 416.5 1346 1.4E+8 1.93 2.52 1.64 6 141.8 97. 163.3 632 8.7E+6 1.99 4.11 1.15 7 21.6 3. 394.7 1222 1.4E+8 2.2 3.75 1.87 8 127.6 19.5 22.2 712 1.5E+7 1.87 3.16 1.58 9 1.3 2. 239.7 947 4.2E+7 3.5 9.8 2.39 1 44.7 2. 84.2 283 1.2E+6 2.3 3.2 1.88 11 118.2 67. 126.8 439 2.7E+6 1.33 1.23 1.7 12 153.1 123.5 146. 496 3.8E+6 1.24.93.95
Table B.8 Summary Statistics for Subbasin 8 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 111.3 16. 79.3 278 2.4E+5.48 -.71.71 2 135.6 99.5 132.4 519 4.1E+6 1.75 3.32.98 3 196.2 17.5 113.3 397 5.9E+5.41-1.5.58 4 174.2 151.5 131.3 532 2.7E+6 1.19 1.96.75 5 171.3 78. 239. 761 2.2E+7 1.63 1.54 1.4 6 17.8 18.5 213.3 95 2.5E+7 2.57 8.36 1.25 7 1.4 54. 145.2 552 6.9E+6 2.25 5.23 1.45 8 57.4 12.5 78.9 227 5.8E+5 1.18 -.4 1.37 9 87.3 1.5 159.8 585 9.1E+6 2.23 4.96 1.83 1 7. 2.5 13.9 43 4.3E+6 1.92 2.43 1.87 11 131.6 12. 114.9 344 9.5E+5.63 -.9.87 12 143. 113. 121.6 436 2.E+6 1.8.66.85
Table B.9 Summary Statistics for Subbasin 9 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 21.1 17. 18.3 6 4.9E+3.8 -.21.87 2 21.1 18. 17.4 59 3.6E+3.68 -.29.83 3 37.1 31.5 25.9 84 7.9E+3.45 -.84.7 4 34.4 35.5 23. 77.E+. -.79.67 5 36.7 1.5 53.5 197 2.9E+5 1.91 3.72 1.46 6 27.1 22.5 26. 87 1.7E+4.97.2.96 7 22.1 8.5 27.4 91 2.7E+4 1.33 1.9 1.24 8 17.8 2. 28.1 87 3.5E+4 1.57 1.38 1.57 9 24.8 4.5 45.4 16 2.1E+5 2.19 4.17 1.83 1 15.1.5 26.8 86 3.6E+4 1.88 2.5 1.77 11 21.9 15. 21.4 7 8.5E+3.87 -.21.97 12 26.3 23. 21.5 79 8.2E+3.82.49.82
Table B.1 Summary Statistics for Subbasin 1 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 1.7 1. 2. 6 1.2E+1 1.48 1.49 1.19 2 3.7 2. 5.2 18 2.9E+2 2.4 3.56 1.4 3 5.3 3. 4.6 14 9.2E+1.98 -.42.87 4 4.7 3. 5. 18 1.8E+2 1.49 2.53 1.7 5 4.7. 8.7 28 1.3E+3 1.97 2.98 1.84 6 2.2. 5. 19 3.9E+2 3.5 9.87 2.29 7 2.1. 4.8 16 2.6E+2 2.39 5.22 2.3 8.8. 1.7 6 1.2E+1 2.65 7.31 2.7 9 1.. 3.6 14 1.8E+2 3.84 14.81 3.61 1 1 1.3. 3. 9 6.E+1 2.17 3.5 2.26 11 1.5. 2. 6 7.9E+.99 -.11 1.36 12 3.5 1. 4.5 14 1.2E+2 1.35.83 1.29 1 Statistics based on a record period of 15 years.
Table B.11 Summary Statistics for Subbasin 11 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 18.4 15. 12.7 44 9.2E+2.46 -.82.69 2 2.8 18. 17.1 63 5.3E+3 1.7.93.82 3 35.4 24.5 24.6 78 1.E+4.68-1.19.69 4 27.6 3.5 18.4 74 3.2E+3.51.96.67 5 31.3 9. 49.3 173 2.4E+5 2.2 3.51 1.57 6 41.8 19.5 74.9 326 1.5E+6 3.55 13.8 1.79 7 21.8 3.5 38. 135 1.3E+5 2.31 4.84 1.74 8 11.2 1. 16.6 51 6.3E+3 1.38.65 1.48 9 16.2.5 29. 98 4.9E+4 1.99 3.15 1.79 1 14.2.5 28.3 9 4.6E+4 2.1 2.75 2. 11 24.1 15.5 23.4 71 1.2E+4.96 -.28.97 12 24.1 18.5 22.9 83 1.6E+4 1.36 1.31.95
Table B.12 Summary Statistics for Subbasin 12 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 32.7 33. 22.7 66 2.E+3.17-1.42.69 2 41.7 23.5 6.9 267 7.5E+5 3.3 12.17 1.46 3 66.7 49.5 5.8 187 1.7E+5 1.33 1.26.76 4 52.6 47. 4.2 169 8.8E+4 1.35 3.17.76 5 88.4 14. 168.2 521 1.1E+7 2.21 3.83 1.9 6 16.1 34.5 298.6 1294 1.1E+8 4.14 17.4 2.81 7 4.3 21.5 65.8 267 8.E+5 2.79 8.6 1.63 8 17.9 7.5 25. 77 2.4E+4 1.55 1.45 1.39 9 24.7 1. 39.2 116 8.5E+4 1.42.53 1.59 1 18. 2.5 34.8 134 1.1E+5 2.61 7.19 1.93 11 41.7 33.5 38.4 122 5.1E+4.91 -.23.92 12 43.7 32. 43.7 176 1.5E+5 1.8 4.3 1.
Table B.13 Summary Statistics for Subbasin 13 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 63.8 66.5 45.8 187 9.9E+4 1.3 1.69.72 2 88.8 68.5 78.1 255 6.1E+5 1.28.76.88 3 17.8 99. 59.4 224 1.2E+5.56 -.37.55 4 9.7 98.5 56.7 194-1.5E+4 -.8 -.92.63 5 149.1 59. 236.9 721 2.4E+7 1.81 1.85 1.59 6 63.4 29. 76.2 245 5.1E+5 1.16.24 1.2 7 67.9 1. 125.1 516 5.9E+6 3.2 1.33 1.84 8 59.9 23. 115.9 489 5.2E+6 3.34 12.25 1.94 9 51.2. 122.2 465 5.2E+6 2.87 8.21 2.39 1 29.8.5 53.5 177 3.E+5 1.98 3.2 1.79 11 65.6 53.5 54.9 176 9.6E+4.58 -.64.84 12 98.7 78. 91. 346 1.E+6 1.39 2.1.92
Table B.14 Summary Statistics for Subbasin 14 Month Average Median Standard Deviation Maximum Skewness Skewness Coefficient Kurtosis Variation Coefficient 1 97.7 11.5 68.1 25 1.9E+5.59 -.1.7 2 147.2 11.5 152.4 597 7.E+6 1.97 4.3 1.4 3 187.7 156. 117.1 431 1.2E+6.76 -.44.62 4 133.4 131. 16.1 367 8.6E+5.72 -.1.8 5 179.9 44.5 276. 852 3.6E+7 1.7 1.65 1.53 6 97.2 36.5 129.7 45 3.E+6 1.38.71 1.33 7 117.2 23. 194.8 719 1.6E+7 2.23 4.84 1.66 8 127.4 31. 212.7 876 2.7E+7 2.81 9.38 1.67 9 65.6 3. 142.8 54 8.2E+6 2.8 7.7 2.18 1 55.2 3.5 18.4 326 2.5E+6 1.94 2.29 1.96 11 114.3 92.5 19.8 315 8.4E+5.63 -.99.96 12 139.1 13. 125.8 397 1.8E+6.92 -.12.9
APPENDIX C Streamflow Duration Curves
6 5 Monthly Peak Flow (cfs) 4 3 2 1 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.1. Streamflow Duration Curve for Subbasin 1 Data
5 4 Monthly Peak Flow (cfs) 3 2 1 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.2. Streamflow Duration Curve for Subbasin 2 Data
6 5 Monthly Peak Flow (cfs) 4 3 2 1 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.3. Streamflow Duration Curve for Subbasin 3 Data
2 16 Monthly Peak Flow (cfs) 12 8 4 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.4. Streamflow Duration Curve for Subbasin 4 Data
2 16 Monthly Peak Flow (cfs) 12 8 4 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.5. Streamflow Duration Curve for Subbasin 5 Data
7 6 Monthly Peak Flow (cfs) 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.6. Streamflow Duration Curve for Subbasin 6 Data
14 12 Monthly Peak Flow (cfs) 1 8 6 4 2 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.7. Streamflow Duration Curve for Subbasin 7 Data
1 8 Monthly Peak Flow (cfs) 6 4 2 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.8. Streamflow Duration Curve for Subbasin 8 Data
25 2 Monthly Peak Flow (cfs) 15 1 5 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.9. Streamflow Duration Curve for Subbasin 9 Data
3 25 Monthly Peak Flow (cfs) 2 15 1 5 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.1. Streamflow Duration Curve for Subbasin 1 Data
35 3 Monthly Peak Flow (cfs) 25 2 15 1 5 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.11. Streamflow Duration Curve for Subbasin 11 Data
14 12 Monthly Peak Flow (cfs) 1 8 6 4 2 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.12. Streamflow Duration Curve for Subbasin 12 Data
8 7 6 Monthly Peak Flow (cfs) 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.13. Streamflow Duration Curve for Subbasin 13 Data
1 8 Monthly Peak Flow (cfs) 6 4 2 1 2 3 4 5 6 7 8 9 1 Exceedance Probability (%) Figure C.14. Streamflow Duration Curve for Subbasin 14 Data
APPENDIX D Streamflow Frequency Histograms
18 15 12 Frequency 9 6 3 6 12 18 24 3 36 42 48 54 6 Monthly Peak Flow (cfs) Figure D.1. Frequency Histogram for Subbasin 1 Streamflow Data with Fitted Distribution
18 15 12 Frequency 9 6 3 6 12 18 24 3 36 42 48 Monthly Peak Flow (cfs) Figure D.2. Frequency Histogram for Subbasin 2 Streamflow Data with Fitted Distribution
18 15 12 Frequency 9 6 3 6 12 18 24 3 36 42 48 54 6 Monthly Peak Flow (cfs) Figure D.3. Frequency Histogram for Subbasin 3 Streamflow Data with Fitted Distribution
15 12 Frequency 9 6 3 2 4 6 8 1 12 14 16 18 2 Monthly Peak Flow (cfs) Figure D.4. Frequency Histogram for Subbasin 4 Streamflow Data with Fitted Distribution
15 12 Frequency 9 6 3 2 4 6 8 1 12 14 16 18 2 Monthly Peak Flow (cfs) Figure D.5. Frequency Histogram for Subbasin 5 Streamflow Data with Fitted Distribution
12 9 Frequency 6 3 2 4 6 Monthly Peak Flow (cfs) Figure D.6. Frequency Histogram for Subbasin 6 Streamflow Data with Fitted Distribution
15 12 Frequency 9 6 3 15 3 45 6 75 9 15 12 135 15 Monthly Peak Flow (cfs) Figure D.7. Frequency Histogram for Subbasin 7 Streamflow Data with Fitted Distribution
15 12 Frequency 9 6 3 1 2 3 4 5 6 7 8 9 1 Monthly Peak Flow (cfs) Figure D.8. Frequency Histogram for Subbasin 8 Streamflow Data with Fitted Distribution
12 9 Frequency 6 3 2 4 6 8 1 12 14 16 18 2 Monthly Peak Flow (cfs) Figure D.9. Frequency Histogram for Subbasin 9 Streamflow Data with Fitted Distribution
12 9 Frequency 6 3 3 6 9 12 15 18 21 24 27 3 Monthly Peak Flow (cfs) Figure D.1. Frequency Histogram for Subbasin 1 Streamflow Data with Fitted Distribution
18 15 12 Frequency 9 6 3 35 7 15 14 175 21 245 28 315 35 Monthly Peak Flow (cfs) Figure D.11. Frequency Histogram for Subbasin 11 Streamflow Data with Fitted Distribution
21 18 15 Frequency 12 9 6 3 15 3 45 6 75 9 15 12 135 15 Monthly Peak Flow (cfs) Figure D.12. Frequency Histogram for Subbasin 12 Streamflow Data with Fitted Distribution
18 15 12 Frequency 9 6 3 1 2 3 4 5 6 7 8 9 1 Monthly Peak Flow (cfs) Figure D.13. Frequency Histogram for Subbasin 13 Streamflow Data with Fitted Distribution
12 9 Frequency 6 3 1 2 3 4 5 6 7 8 9 1 Monthly Peak Flow (cfs) Figure D.14. Frequency Histogram for Subbasin 14 Streamflow Data with Fitted Distribution
APPENDIX E Chi-Square Goodness of Fit Test Results
Subbasin ID 2 χ c Table E.1 Results for the Chi-Square Goodness of Fit Test Degrees 2 χ 1 α, ν for Selected Confidence Intervals of Freedom 9% 95% 97.5% 99% 99.5% 1 21.1 13 19.8 22.4 24.7 27.7 29.8 2 16. 14 21.1 23.7 26.1 29.1 31.3 3 15.1 13 19.8 22.4 24.7 27.7 29.8 4 7.2 12 18.5 21. 23.3 26.2 28.3 5 8.6 13 19.8 22.4 24.7 27.7 29.8 6 6.4 12 18.5 21. 23.3 26.2 28.3 7 1.7 12 18.5 21. 23.3 26.2 28.3 8 5.8 12 18.5 21. 23.3 26.2 28.3 9 1. 9 14.7 16.9 19. 21.7 23.6 11 5.8 9 14.7 16.9 19. 21.7 23.6 12 7.4 1 16. 18.3 2.5 23.2 25.2 13 1.2 12 18.5 21. 23.3 26.2 28.3 14 7.4 12 18.5 21. 23.3 26.2 28.3
APPENDIX F Regression Plots for Other Subbasin Geomorphic Attributes
1 8 Flow (cfs) 6 4 2 4 5 6 7 8 9 1 11 L o (ft) Figure F.1. Regression Analysis Results on Average Overland Flow Length (L o )
1 8 Flow (cfs) 6 4 2.25.3.35.4.45.5 So (ft/ft) Figure F.2. Regression Analysis Results on Basin Overland Slope (S o )
1 8 Flow (cfs) 6 4 2..5 1. 1.5 2. 2.5 3. L (mi) Figure F.3. Regression Analysis Results on Basin Length along Main Channel from Outlet to Upstream Boundary (L)
1 8 Flow (cfs) 6 4 2..5.1.15.2.25 S (mi/mi) Figure F.4. Regression Analysis Results on Basin Slope along Main Channel from Outlet to Upstream Boundary (S)
9 8 7 6 Flow (cfs) 5 4 3 2 1..2.4.6.8 1. 1.2 Lca (mi) Figure F.5. Regression Analysis Results on Basin Length along Main Channel from Outlet to Point Opposite Centroid (L ca )
1 8 Flow (cfs) 6 4 2..5.1.15.2.25 Sca (mi/mi) Figure F.6. Regression Analysis Results on Basin Slope along Main Channel from Outlet to Point Opposite Centroid (S ca )
1 8 Flow (cfs) 6 4 2..5 1. 1.5 2. 2.5 Lc (mi) Figure F.7. Regression Analysis Results on Maximum Flow (watercourse) Length (L c )
1 8 Flow (cfs) 6 4 2..5.1.15.2.25 Sc (mi/mi) Figure F.8. Regression Analysis Results on Maximum Flow (watercourse) Slope (S c )
Determination of Variance for APPENDIX G qˆ p to Construct Confidence Intervals
The variance of the predicted flow values as expressed in Equation (11) must be estimated in order to construct the confidence bands. The variance operator is applied to the expression for predicted flows: VAR 1 ( qˆ ) VAR ln P( q > q ) p λ [ ] = o Noting that 1 = λ Q, it is obtained 2 ( qˆ ) = VAR( Q) ln P( q q ) p [ ] VAR > o and VAR ( Q) = VAR( Q). The regression equation relating Q to catchment properties is nonlinear. To find the variance of the mean flow the regression equation must be linearized. This is achieved by taking the logarithm on both sides of the power function expressed in Equation (1), yielding log Q = log c + blog A d The regression parameters, c and b, are known. The drainage area is available for most of the basins or it can be easily obtained by different methods. Therefore, the value of logq can be determined. Likewise, the variance of logq can be calculated.
Then, a relation between the VAR (logq ) and VAR (Q ) should be established. This relationship was performed developing a Taylor expansion for logq. The results of the Taylor series were expressed as VAR 2 ( Q) = ( Q ln 1) VAR ( log Q) Finally, the variance of can be calculated using the following equation. VAR 2 2 ( qˆ ) = ln [ P( q > q )] ( Q ln 1) VAR ( log Q) p o