Statistical Approach for Computing Base Flow Rates in Gaged Rivers and Hydropower Effect Analysis
Abstract
:1. Introduction
2. Case Study
3. Materials and Methods
3.1. Available Information
3.2. Base Flow Determination
3.2.1. Base Flow Obtained from the Recorded Maximum Floods
3.2.2. Based on the Multiannual Monthly Mean Flow Series
3.2.3. Statistical Approximation
Mean Squared Error (MSE)
Chi-Square
Confidence Intervals
3.2.4. Flowchart
4. Results
4.1. Estimated Base Flow Qb Obtained from the Record of Maximum Flood Hydrographs
4.2. Trend Analysis of the Multivariate Monthly Mean Flow Series Was Performed–Qmm,Tr
4.3. Statistical Approximation
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
A.O. | Condition before the operation of Urrá 1 Hydroelectric Power Plant |
Expected value. | |
D.O. | Condition after the operation of Urrá 1 Hydroelectric Power Plant |
Upper confidence limit. | |
k | Shape parameter |
Mean squared error (MSE) (%) | |
Sample | |
Observed value | |
Probability of occurrence | |
Exceedance period. | |
The recorded flow (m3/s) | |
Direct runoff flow (m3/s) | |
Qb | Base Flow (m3/s) |
Qb,Tr | Base flow for different return periods (m3/s) |
Qmm | Multiannual monthly mean flow (m3/s) |
Qmm,Tr | Multiannual monthly mean flow for different return periods (m3/s) |
Standard deviation | |
Smoothed value | |
Time | |
Lower confidence limit. | |
Observed value | |
Normal distribution of | |
Location parameter | |
Scale parameter. | |
Unknown parameter | |
Smoothing constant | |
Gamma function | |
Chi-square, | |
Confidence level. |
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Year | Qb (m3/s) | Scenario | Year | Qb (m3/s) | Scenario |
---|---|---|---|---|---|
1970 | 602.5 | A.O | 1996 | 774.3 | A.O |
1971 | 465.8 | A.O | 1997 | 376.6 | A.O |
1972 | 590.0 | A.O | 1998 | 680.2 | A.O |
1973 | 511.8 | A.O | 1999 | 596.0 | A.O |
1974 | 503.0 | A.O | 2000 | 452.8 | D.O |
1975 | 646.6 | A.O | 2001 | 575.0 | D.O |
1976 | A.O | 2002 | 606.5 | D.O | |
1977 | 398.0 | A.O | 2003 | 592.5 | D.O |
1978 | 548.0 | A.O | 2004 | 314.5 | D.O |
1979 | 588.4 | A.O | 2005 | 205.0 | D.O |
1980 | 458.0 | A.O | 2006 | 284.0 | D.O |
1981 | 719.2 | A.O | 2007 | 620.5 | D.O |
1982 | 494.0 | A.O | 2008 | 561.4 | D.O |
1983 | 438.0 | A.O | 2009 | 594.3 | D.O |
1984 | 516.4 | A.O | 2010 | 554.1 | D.O |
1985 | 377.0 | A.O | 2011 | 300.5 | D.O |
1986 | 604.4 | A.O | 2012 | 626.3 | D.O |
1987 | 463.9 | A.O | 2013 | 602.8 | D.O |
1988 | 774.8 | A.O | 2014 | 478.0 | D.O |
1989 | 474.4 | A.O | 2015 | 212.8 | D.O |
1990 | 570.6 | A.O | 2016 | 390.5 | D.O |
1991 | 507.5 | A.O | 2017 | 765.0 | D.O |
1992 | 507.5 | A.O | 2018 | 726.8 | D.O |
1993 | 493.6 | A.O | 2019 | 555.2 | D.O |
1994 | 333.1 | A.O | 2020 | 654.7 | D.O |
1995 | 479.8 | A.O | 2021 | 594.8 | D.O |
Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1970 | 662.4 | 679.7 | 549.2 | 578.4 | ||||||||
1971 | 425.5 | 211.3 | 366.7 | 258.1 | 508.7 | 491.4 | 636.0 | 522.0 | 590.5 | 627.1 | 540.9 | 226.0 |
1972 | 244.5 | 132.0 | 105.9 | 562.7 | 582.3 | 432.1 | 457.7 | 525.1 | 606.1 | 490.5 | 278.3 | |
1973 | 126.1 | 63.1 | 48.1 | 230.9 | 382.3 | 530.1 | 514.5 | 528.4 | 562.6 | 688.3 | 479.3 | |
1974 | 332.1 | 134.4 | 120.4 | 191.9 | 489.8 | 528.5 | 387.7 | 442.5 | 489.8 | 665.9 | 704.8 | 272.0 |
1975 | 111.0 | 70.0 | 72.0 | 69.2 | 232.7 | 383.5 | 710.6 | 700.5 | 658.0 | 726.9 | 698.5 | 514.2 |
1976 | 162.4 | 133.9 | 91.5 | 136.9 | 338.7 | 570.1 | 599.2 | 382.3 | 388.2 | 559.5 | 445.6 | 167.6 |
1977 | 108.3 | 69.0 | 50.6 | 103.5 | 356.0 | 577.9 | 562.3 | 568.2 | 442.5 | 581.7 | 500.2 | 329.7 |
1978 | 121.5 | 119.0 | 135.2 | 378.9 | 548.7 | 722.5 | 499.6 | 586.4 | 482.2 | 612.3 | 567.2 | 348.6 |
1979 | 110.8 | 72.1 | 74.4 | 137.2 | 366.7 | 527.7 | 508.6 | 398.4 | 476.8 | 488.1 | 338.5 | 263.1 |
1980 | 144.3 | 137.0 | 58.7 | 66.9 | 232.6 | 362.6 | 463.4 | 472.1 | 557.1 | 392.6 | 360.3 | |
1981 | 203.9 | 223.6 | 379.0 | 313.5 | 637.9 | 690.3 | 576.6 | 509.8 | 725.8 | 529.0 | 434.3 | 320.8 |
1982 | 174.1 | 208.0 | 101.4 | 228.5 | 495.5 | 444.0 | 560.9 | 479.6 | 435.9 | 521.3 | 390.1 | 172.1 |
1983 | 106.0 | 67.6 | 81.7 | 184.2 | 360.1 | 509.8 | 475.0 | 452.4 | 476.3 | 502.1 | 459.4 | 328.6 |
1984 | 187.4 | 133.7 | 121.1 | 98.8 | 228.6 | 333.4 | 507.6 | 541.5 | 545.5 | 546.5 | 451.7 | 261.9 |
1985 | 116.5 | 83.5 | 73.4 | 100.0 | 160.0 | 351.3 | 384.0 | 491.0 | 534.0 | 522.2 | 385.0 | 266.5 |
1986 | 130.3 | 147.1 | 84.4 | 420.9 | 437.3 | 439.3 | 626.4 | 267.2 | 377.5 | 479.8 | 373.0 | 219.1 |
1987 | 132.6 | 146.5 | 73.5 | 306.1 | 528.5 | 378.2 | 547.9 | 604.9 | 497.7 | 577.8 | 368.2 | 358.1 |
1988 | 125.4 | 81.9 | 57.2 | 205.6 | 373.0 | 448.7 | 618.4 | 838.8 | 548.0 | 632.6 | 485.5 | 320.4 |
1989 | 247.9 | 112.1 | 155.0 | 150.2 | 411.0 | 522.2 | 494.8 | 471.8 | 452.6 | 459.1 | 393.6 | 284.5 |
1990 | 174.8 | 112.0 | 99.4 | 153.7 | 477.7 | 419.9 | 426.3 | 460.5 | 352.3 | 466.5 | 581.5 | 321.5 |
1991 | 151.2 | 116.3 | 142.1 | 122.6 | 336.9 | 542.6 | 487.7 | 469.9 | 434.5 | 509.2 | 392.1 | 293.9 |
1992 | 116.6 | 67.1 | 77.6 | 80.9 | 304.2 | 338.2 | 396.1 | 532.5 | 500.3 | 471.4 | 390.3 | 312.5 |
1993 | 167.4 | 130.5 | 127.2 | 265.5 | 558.7 | 458.3 | 536.4 | 388.6 | 394.7 | 434.9 | 481.4 | 415.9 |
1994 | 196.5 | 104.1 | 94.6 | 232.3 | 558.9 | 405.6 | 446.7 | 545.2 | 539.5 | 553.8 | 577.1 | 288.2 |
1995 | 138.6 | 161.1 | 320.8 | 480.0 | 588.1 | 489.1 | 544.1 | 547.3 | 426.0 | 289.9 | ||
1996 | 281.5 | 211.8 | 345.7 | 318.2 | 599.5 | 655.3 | 797.0 | 635.1 | 577.9 | 515.9 | 375.5 | 145.4 |
1997 | 139.0 | 191.6 | 114.2 | 142.3 | 310.9 | 474.5 | 460.3 | 363.1 | 318.0 | 416.0 | 370.1 | 185.7 |
1998 | 86.6 | 115.0 | 72.1 | 190.7 | 376.5 | 566.0 | 694.5 | 537.6 | 455.6 | 516.9 | 536.2 | 356.5 |
1999 | 255.4 | 294.7 | 341.1 | 569.6 | 630.5 | 559.1 | 619.1 | 710.8 | 661.7 | 700.2 | 462.5 | 220.6 |
Year | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2000 | 154.9 | 183.1 | 290.0 | 293.3 | 428.3 | 507.2 | 488.9 | 600.0 | 554.0 | 535.2 | 427.0 | 368.7 |
2001 | 271.1 | 222.4 | 276.3 | 269.5 | 318.3 | 465.3 | 462.4 | 405.4 | 342.9 | 430.5 | 569.5 | 417.4 |
2002 | 253.7 | 127.8 | 145.6 | 261.3 | 482.2 | 642.2 | 629.8 | 379.8 | 479.7 | 441.0 | 380.9 | 257.2 |
2003 | 222.7 | 104.8 | 212.2 | 177.7 | 510.5 | 499.6 | 561.1 | 581.2 | 526.0 | 537.0 | 482.1 | 458.8 |
2004 | 197.2 | 153.3 | 241.8 | 219.2 | 324.0 | 552.8 | 506.5 | 376.9 | 450.9 | 357.9 | 410.1 | 279.8 |
2005 | 204.5 | 285.1 | 244.1 | 301.9 | 422.4 | 563.2 | 605.5 | 539.7 | 486.3 | 538.2 | 472.7 | 268.5 |
2006 | 191.3 | 258.9 | 286.4 | 356.2 | 501.3 | 557.4 | 554.4 | 521.4 | 507.7 | 354.2 | 289.8 | 317.4 |
2007 | 163.4 | 194.2 | 213.2 | 321.6 | 527.8 | 653.4 | 795.4 | 740.7 | 694.8 | 570.1 | 394.6 | 215.5 |
2008 | 175.5 | 130.4 | 253.7 | 200.4 | 553.5 | 560.2 | 649.1 | 405.2 | 426.6 | 755.0 | 386.2 | 299.1 |
2009 | 177.5 | 314.1 | 303.7 | 408.7 | 470.3 | 584.5 | 587.1 | 416.2 | 323.5 | 162.9 | 243.0 | 207.3 |
2010 | 129.7 | 140.0 | 242.8 | 292.7 | 361.1 | 610.5 | 414.6 | 614.3 | 641.7 | 492.4 | 446.8 | 633.1 |
2011 | 341.2 | 182.7 | 283.3 | 493.5 | 491.7 | 481.6 | 478.4 | 509.8 | 503.4 | 467.4 | 312.5 | 414.5 |
2012 | 245.3 | 186.4 | 203.2 | 354.6 | 592.0 | 421.8 | 371.9 | 449.7 | 418.9 | 386.5 | 460.8 | 229.1 |
2013 | 169.9 | 164.1 | 303.4 | 442.5 | 379.1 | 334.7 | 290.0 | 474.6 | 570.5 | 398.7 | 293.6 | 227.8 |
2014 | 177.4 | 153.8 | 169.2 | 172.5 | 205.1 | 287.7 | 282.7 | 247.7 | 457.2 | 360.5 | 336.1 | 257.6 |
2015 | 137.0 | 170.6 | 163.1 | 160.0 | 228.7 | 395.8 | 288.1 | 245.9 | 226.3 | 297.5 | 362.6 | 216.8 |
2016 | 160.5 | 151.6 | 156.0 | 154.6 | 283.8 | 551.4 | 577.8 | 427.6 | 297.1 | 276.2 | 433.0 | 410.5 |
2017 | 187.0 | 140.5 | 151.2 | 171.4 | 390.9 | 671.6 | 753.5 | 636.4 | 576.1 | 654.0 | 238.1 | 350.8 |
2018 | 191.1 | 169.8 | 137.3 | 142.3 | 418.4 | 561.5 | 647.3 | 509.5 | 352.2 | 318.4 | 437.6 | 208.0 |
2019 | 135.4 | 140.0 | 129.2 | 151.5 | 288.4 | 642.7 | 432.7 | 466.4 | 333.0 | 397.0 | 389.8 | 160.6 |
2020 | 162.2 | 142.0 | 135.7 | 130.4 | 147.0 | 192.8 | 401.0 | 661.3 | 421.5 | 468.1 | 254.6 | 275.4 |
2021 | 160.2 | 133.8 | 146.1 | 236.0 | 284.2 | 445.9 | 573.1 | 618.4 | 565.9 | 439.8 | 289.6 |
Indicador | Sample | GEV | Gumbel | Pearson Type III | ||
---|---|---|---|---|---|---|
M.L. | L-M. | M.L. | L-M. | M.L. | ||
Asymmetry C. | 0.515 | 0.49 | 0.69 | 1.14 | 1.14 | 0.62 |
Kurtosis C | 2.62 | 3.25 | 3.73 | 2.40 | 2.40 | 3.58 |
X2 | 2.14 | 4.07 | 4.07 | 4.07 | 1.66 |
Indicador | Sample | GEV | Gumbel | Pearson Type III | ||
---|---|---|---|---|---|---|
M.L. | L-M. | M.L. | L-M. | M.L. | ||
Asymmetry C. | −0.651 | 0.757 | −1.09 | 1.14 | 1.14 | 0.96 |
Kurtosis C | 2.10 | 3.51 | 4.46 | 2.40 | 2.40 | 4.39 |
X2 | 7.45 | 11.82 | 9.09 | 20.55 | 110.00 |
Tr | Qb,Tr (m3/s) | |
---|---|---|
Period: 1970–1999 | Period: 2000–2021 | |
100 | 825 | 764 |
50 | 786 | 753 |
20 | 729 | 728 |
10 | 679 | 698 |
5 | 622 | 652 |
Indicator | Sample | GEV | Gumbel | Perarson Type III | ||
---|---|---|---|---|---|---|
M.L. | L-M. | M.L. | L-M. | M.L | ||
January | ||||||
Asymmetry C. | 1.71 | 100 | 9.05 | 1.14 | 1.14 | 1.62 |
Kurtosis C | 5.11 | - | - | 2.40 | 2.40 | 6.93 |
X2 | 2.62 | 3.59 | 5.03 | 9.86 | 4.55 | |
February | ||||||
Asymmetry C. | 1.04 | 2.36 | 1.60 | 1.14 | 1.14 | - |
Kurtosis C | 3.34 | 16.50 | 8.27 | 2.40 | 2.40 | - |
X2 | 13.50 | 13.50 | 9.50 | 9.50 | - | |
March | ||||||
Asymmetry C. | 1.84 | - | - | 1.14 | 1.14 | - |
Kurtosis C | 4.24 | - | - | 2.40 | 2.40 | - |
X2 | 1 | 1 | 8.50 | 17.00 | - | |
April | ||||||
Asymmetry C. | 1.33 | 3.70 | 2.38 | 1.14 | 1.14 | - |
Kurtosis C | 4.14 | 56.50 | 16.90 | 2.40 | 2.40 | - |
X2 | 1.78 | 1.26 | 2.30 | 2.81 | - | |
May | ||||||
Asymmetry C. | −0.01 | −0.40 | 0.0005 | 1.14 | 1.14 | −0.058 |
Kurtosis C | 1.80 | 2.90 | 2.72 | 2.40 | 2.40 | 3.01 |
X2 | 3.59 | 6.97 | 6.48 | 6.48 | 174 | |
June | ||||||
Asymmetry C. | 0.44 | 0.55 | 0.49 | 1.14 | 1.14 | 1.14 |
Kurtosis C | 2.37 | 3.37 | 3.24 | 2.40 | 2.40 | 4.95 |
X2 | 2.62 | 1.66 | 2.14 | 2.14 | 2.14 | |
July | ||||||
Asymmetry C. | 0.59 | 0.67 | 0.64 | 1.14 | 1.14 | 0.93 |
Kurtosis C | 2.79 | 3.68 | 3.58 | 2.40 | 2.40 | 4,31 |
X2 | 3.59 | 1.66 | 1.66 | 1.66 | 1.66 | |
August | ||||||
Asymmetry C. | 0.73 | 0.49 | 0.78 | 1.14 | 1.14 | 0.41 |
Kurtosis C | 3.93 | 3.25 | 3.99 | 2.40 | 2.40 | 3.26 |
X2 | 4.55 | 5.03 | 5.03 | 7.45 | 4.55 | |
September | ||||||
Asymmetry C. | 0.32 | 0.26 | 0.32 | 1.14 | 1.14 | 0.39 |
Kurtosis C | 2.60 | 2.89 | 2.97 | 2.40 | 2.40 | 3.23 |
X2 | 3.59 | 3.59 | 5.52 | 2.62 | 3.59 | |
October | ||||||
Asymmetry C. | 0.49 | 0.52 | 0.68 | 1.14 | 1.14 | 0.70 |
Kurtosis C | 2.45 | 3.31 | 3.70 | 2.40 | 2.40 | 3.74 |
X2 | 1.27 | 1.27 | 1.27 | 3.13 | 1.27 | |
November | ||||||
Asymmetry C. | 0.90 | 3.36 | 1.78 | 1.14 | 1.14 | 1.47 |
Kurtosis C | 2.70 | 40.40 | 9.72 | 2.40 | 2.40 | 6.26 |
X2 | 3.60 | 2.20 | 2.20 | 5.00 | 3.13 | |
December | ||||||
Asymmetry C. | 0.91 | 0.82 | 0.88 | 1.14 | 1.14 | 0.81 |
Kurtosis C | 3.69 | 4.11 | 4.31 | 2.40 | 2.40 | 3.99 |
X2 | 2.67 | 2.67 | 2.67 | 2.67 | 2.67 |
Indicator | Sample | GEV | Gumbel | Perarson Type III | ||
---|---|---|---|---|---|---|
M.L. | L-M. | M.L. | L-M. | M.L. | ||
January | ||||||
Asymmetry C. | 1.49 | 2.57 | 3.07 | 1.14 | 1.14 | 1.56 |
Kurtosis C | 4.40 | 20.00 | 31.40 | 2.40 | 2.40 | 6.63 |
X2 | 1.45 | 0.91 | 1.45 | 1.45 | 2.55 | |
February | ||||||
Asymmetry C. | 1.40 | 3.00 | 4.46 | 1.14 | 1.14 | 1.27 |
Kurtosis C | 3.62 | 21.10 | 128 | 2.40 | 2.40 | 5.42 |
X2 | 0.91 | 0.91 | 1.45 | 4.73 | 3.62 | |
March | ||||||
Asymmetry C. | 0.07 | −1.00 | 0.16 | 1.14 | 1.14 | - |
Kurtosis C | 1.36 | 3.78 | 2.80 | 2.40 | 2.40 | - |
X2 | 5.27 | 4.73 | 5.82 | 6.91 | - | |
April | ||||||
Asymmetry C. | 0.70 | 3.00 | 1.31 | 1.14 | 1.14 | - |
Kurtosis C | 2.25 | 37.10 | 6.33 | 2.40 | 2.40 | - |
X2 | 2.00 | 2.55 | 2.55 | 2,55 | - | |
May | ||||||
Asymmetry C. | −0.27 | −0.57 | −0.39 | 1.14 | 1.14 | −0.73 |
Kurtosis C | 1.97 | 3.14 | 2.90 | 2.40 | 2.40 | 3.79 |
X2 | 0.91 | 1.45 | 3.09 | 1.45 | 110 | |
June | ||||||
Asymmetry C. | −0.99 | −1.28 | −1.21 | 1.14 | 1.14 | −1.53 |
Kurtosis C | 3.02 | 5.15 | 4.87 | 2.40 | 2.40 | 6.52 |
X2 | 2.55 | 2.55 | 11.27 | 6.91 | 110 | |
July | ||||||
Asymmetry C. | 0.01 | −0.07 | −0.10 | 1.14 | 1.14 | 0.02 |
Kurtosis C | 2.18 | 2.71 | 2.71 | 2.40 | 2.40 | 3.00 |
X2 | 1.45 | 1.45 | 4.18 | 4.18 | 2.55 | |
August | ||||||
Asymmetry C. | −0.14 | −0.21 | −0.10 | 1.14 | 1.14 | −0.20 |
Kurtosis C | 2.35 | 2.75 | 2.71 | 2.40 | 2.40 | 3.06 |
X2 | 2.55 | 2.55 | 2.55 | 2.00 | 110 | |
September | ||||||
Asymmetry C. | −0.05 | −0.13 | −0.13 | 1.14 | 1.14 | −0.08 |
Kurtosis C | 2.23 | 2.72 | 2.72 | 2.40 | 2.40 | 3.01 |
X2 | 3.09 | 4.18 | 3.64 | 4.18 | 110 | |
October | ||||||
Asymmetry C. | 0.37 | 0.27 | 0.39 | 1.14 | 1.14 | 0.27 |
Kurtosis C | 3.10 | 2.90 | 3.06 | 2.40 | 2.40 | 3.11 |
X2 | 0.36 | 0.91 | 2.00 | 0.91 | 0.36 | |
November | ||||||
Asymmetry C. | 0.09 | 0.08 | 0.08 | 1.14 | 1.14 | 0.18 |
Kurtosis C | 2.71 | 2.74 | 2.71 | 2.40 | 2.40 | 3.05 |
X2 | 5.27 | 3.64 | 2.55 | 4.18 | 3.64 | |
December | ||||||
Asymmetry C. | 1.34 | 2.56 | 2.51 | 1.14 | 1.14 | 1.33 |
Kurtosis C | 4.03 | 19.80 | 19.00 | 2.40 | 2.40 | 5.67 |
X2 | 2.71 | 2.71 | 2.71 | 6.14 | 2.71 |
Tr | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
100 | 417 | 314 | 337 | 543 | 656 | 772 | 825 | 839 | 752 | 756 | 825 | 595 |
50 | 373 | 282 | 300 | 484 | 640 | 734 | 784 | 789 | 722 | 728 | 764 | 549 |
20 | 314 | 240 | 250 | 405 | 609 | 678 | 724 | 718 | 676 | 687 | 681 | 486 |
10 | 268 | 207 | 212 | 345 | 575 | 630 | 674 | 661 | 635 | 652 | 616 | 434 |
5 | 221 | 173 | 172 | 281 | 528 | 574 | 618 | 598 | 585 | 612 | 548 | 379 |
Tr | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
100 | 361 | 334 | 365 | 664 | 626 | 677 | 825 | 769 | 715 | 778 | 571 | 658 |
50 | 331 | 307 | 348 | 605 | 610 | 672 | 798 | 745 | 693 | 736 | 553 | 598 |
20 | 290 | 270 | 322 | 465 | 580 | 661 | 751 | 702 | 655 | 671 | 523 | 517 |
10 | 258 | 241 | 297 | 403 | 546 | 645 | 704 | 660 | 617 | 614 | 494 | 453 |
5 | 225 | 211 | 267 | 338 | 502 | 618 | 642 | 605 | 567 | 546 | 455 | 385 |
Tr | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
100 | 49.45 | 61.94 | 59.15 | 34.18 | 20.48 | 6.42 | 0.00 | 1.70 | 8.85 | 8.36 | 0.00 | 27.88 |
50 | 52.54 | 64.12 | 61.83 | 38.42 | 18.58 | 6.62 | 0.25 | 0.38 | 8.14 | 7.38 | 2.80 | 30.15 |
20 | 56.93 | 67.08 | 65.71 | 44.44 | 16.46 | 7.00 | 0.69 | 1.51 | 7.27 | 5.76 | 6.28 | 33.33 |
10 | 60.53 | 69.51 | 68.78 | 49.19 | 15.32 | 7.22 | 0.74 | 2.65 | 6.48 | 3.98 | 9.28 | 36.08 |
5 | 64.47 | 72.19 | 72.35 | 54.82 | 15.11 | 7.72 | 0.64 | 3.86 | 5.95 | 1.61 | 11.90 | 39.07 |
MSE | 57.04 | 67.07 | 65.73 | 44.82 | 17.21 | 7.01 | 0.55 | 2.33 | 7.41 | 5.93 | 7.47 | 33.54 |
Tr | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
100 | 52,75 | 56.28 | 52.23 | 20.81 | 18.06 | 11.39 | 7.98 | 0.65 | 6.41 | 1.83 | 25.26 | 13.87 |
50 | 56.04 | 59.23 | 53.78 | 27.62 | 18.99 | 10.76 | 5.98 | 1.06 | 7.97 | 2.26 | 26.56 | 20.58 |
20 | 60.16 | 62.91 | 55.77 | 36.13 | 20.33 | 9.10 | 3.16 | 3.57 | 10.03 | 7.83 | 28.16 | 28.98 |
10 | 63.04 | 65.47 | 57.45 | 42.26 | 21.49 | 7.59 | 0.86 | 5.44 | 11.60 | 12.03 | 29.23 | 35.10 |
5 | 65.49 | 67.64 | 59.05 | 48.16 | 23.01 | 5.21 | 1.53 | 7.21 | 13.04 | 16.06 | 30.21 | 40.95 |
MSE | 59.68 | 62.44 | 55.71 | 36.35 | 20.45 | 9.11 | 4.74 | 4.38 | 10.10 | 9.79 | 27.94 | 29.55 |
Tr (Years) | Qb,Tr (m3/s) | Qmm,Tr (m3/s) | E (%) | |||
---|---|---|---|---|---|---|
Period | ||||||
1970–1999 | 2000–2021 | 1970–1999 | 2000–2021 | 1970–1999 | 2000–2021 | |
100 | 825 | 764 | 825 | 769 | 0.00% | 0.65% |
50 | 786 | 753 | 784 | 745 | 0.25% | 1.06% |
20 | 729 | 728 | 724 | 702 | 0.69% | 3.57% |
10 | 679 | 698 | 674 | 660 | 0.74% | 5.44% |
5 | 622 | 652 | 618 | 605 | 0.64% | 7.21% |
MSE | 0.55% | 4.38% |
Tr (Years) | Qb,Tr (m3/s) | Qmm,Tr (m3/s) | X2 | |||
---|---|---|---|---|---|---|
Period | ||||||
1970–1999 | 2000–2021 | 1970–1999 | 2000–2021 | 1970–1999 | 2000–2021 | |
100 | 825 | 764 | 825 | 769 | 0.00 | 0.03 |
50 | 786 | 753 | 784 | 745 | 0.01 | 0.08 |
20 | 729 | 728 | 724 | 702 | 0.03 | 0.93 |
10 | 679 | 698 | 674 | 660 | 0.04 | 2.07 |
5 | 622 | 652 | 618 | 605 | 0.03 | 3.39 |
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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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Villalba-Barrios, A.F.; Coronado-Hernández, O.E.; Fuertes-Miquel, V.S.; Coronado-Hernández, J.R.; Ramos, H.M. Statistical Approach for Computing Base Flow Rates in Gaged Rivers and Hydropower Effect Analysis. Hydrology 2023, 10, 137. https://doi.org/10.3390/hydrology10070137
Villalba-Barrios AF, Coronado-Hernández OE, Fuertes-Miquel VS, Coronado-Hernández JR, Ramos HM. Statistical Approach for Computing Base Flow Rates in Gaged Rivers and Hydropower Effect Analysis. Hydrology. 2023; 10(7):137. https://doi.org/10.3390/hydrology10070137
Chicago/Turabian StyleVillalba-Barrios, Andrés F., Oscar E. Coronado-Hernández, Vicente S. Fuertes-Miquel, Jairo R. Coronado-Hernández, and Helena M. Ramos. 2023. "Statistical Approach for Computing Base Flow Rates in Gaged Rivers and Hydropower Effect Analysis" Hydrology 10, no. 7: 137. https://doi.org/10.3390/hydrology10070137