Figure 1.
Description of Location, SRTM-DEM (Shuttle Radar Topography Mission–digital elevation model, meters) and flow gauge stations for the Kabul River basin (KRB), Pakistan.
Figure 1.
Description of Location, SRTM-DEM (Shuttle Radar Topography Mission–digital elevation model, meters) and flow gauge stations for the Kabul River basin (KRB), Pakistan.
Figure 2.
Spatial distribution of trends in the annual maximum flood regime of the KRB, Pakistan.
Figure 2.
Spatial distribution of trends in the annual maximum flood regime of the KRB, Pakistan.
Figure 3.
Comparison between non-stationary and stationary flood frequency curves (FFCs) at site 5, along with non-stationary uncertainty bounds for the year 2016.
Figure 3.
Comparison between non-stationary and stationary flood frequency curves (FFCs) at site 5, along with non-stationary uncertainty bounds for the year 2016.
Figure 4.
Comparison between non-stationary and stationary FFCs at site 11, along with non-stationary uncertainty bounds for the year 2016.
Figure 4.
Comparison between non-stationary and stationary FFCs at site 11, along with non-stationary uncertainty bounds for the year 2016.
Figure 5.
Comparison between non-stationary and stationary FFCs at site 18, along with non-stationary uncertainty bounds for the year 2016.
Figure 5.
Comparison between non-stationary and stationary FFCs at site 18, along with non-stationary uncertainty bounds for the year 2016.
Figure 6.
Comparison between non-stationary and stationary FFCs at site 21, along with non-stationary uncertainty bounds for the year 2016.
Figure 6.
Comparison between non-stationary and stationary FFCs at site 21, along with non-stationary uncertainty bounds for the year 2016.
Figure 7.
Comparison between non-stationary and stationary FFCs at site 22, along with non-stationary uncertainty bounds for the year 2016.
Figure 7.
Comparison between non-stationary and stationary FFCs at site 22, along with non-stationary uncertainty bounds for the year 2016.
Figure 8.
Comparison between non-stationary and stationary FFCs at site 24, along with non-stationary uncertainty bounds for the year 2016.
Figure 8.
Comparison between non-stationary and stationary FFCs at site 24, along with non-stationary uncertainty bounds for the year 2016.
Figure 9.
Comparison between non-stationary and stationary FFCs at site 6, along with non-stationary uncertainty bounds for the year 2013.
Figure 9.
Comparison between non-stationary and stationary FFCs at site 6, along with non-stationary uncertainty bounds for the year 2013.
Figure 10.
Comparison between non-stationary and stationary FFCs at site 19, along with non-stationary uncertainty bounds for the year 2016.
Figure 10.
Comparison between non-stationary and stationary FFCs at site 19, along with non-stationary uncertainty bounds for the year 2016.
Figure 11.
Comparison between non-stationary and stationary FFCs at site 9, along with non-stationary uncertainty bounds for the year 2009.
Figure 11.
Comparison between non-stationary and stationary FFCs at site 9, along with non-stationary uncertainty bounds for the year 2009.
Figure 12.
Comparison between non-stationary and stationary FFCs at site 16, along with non-stationary uncertainty bounds for the year 2016.
Figure 12.
Comparison between non-stationary and stationary FFCs at site 16, along with non-stationary uncertainty bounds for the year 2016.
Figure 13.
FFCs at site 5, along with stationary uncertainty bounds for the year 2009.
Figure 13.
FFCs at site 5, along with stationary uncertainty bounds for the year 2009.
Figure 14.
Comparison between non-stationary and stationary FFCs at site 6, along with non-stationary uncertainty bounds for the year 2004.
Figure 14.
Comparison between non-stationary and stationary FFCs at site 6, along with non-stationary uncertainty bounds for the year 2004.
Figure 15.
FFCs at site 9, along with stationary uncertainty bounds for the year 1991.
Figure 15.
FFCs at site 9, along with stationary uncertainty bounds for the year 1991.
Figure 16.
Comparison between non-stationary and stationary FFCs at site 11, along with non-stationary uncertainty bounds for the year 2015.
Figure 16.
Comparison between non-stationary and stationary FFCs at site 11, along with non-stationary uncertainty bounds for the year 2015.
Figure 17.
FFCs at site 16, along with stationary uncertainty bounds for the year 2009.
Figure 17.
FFCs at site 16, along with stationary uncertainty bounds for the year 2009.
Figure 18.
Comparison between non-stationary and stationary FFCs at site 18, along with non-stationary uncertainty bounds for the year 2009.
Figure 18.
Comparison between non-stationary and stationary FFCs at site 18, along with non-stationary uncertainty bounds for the year 2009.
Figure 19.
Comparison between non-stationary and stationary FFCs at site 19, along with non-stationary uncertainty bounds for the year 2009.
Figure 19.
Comparison between non-stationary and stationary FFCs at site 19, along with non-stationary uncertainty bounds for the year 2009.
Figure 20.
Comparison between non-stationary and stationary FFCs at site 21, along with non-stationary uncertainty bounds for the year 2009.
Figure 20.
Comparison between non-stationary and stationary FFCs at site 21, along with non-stationary uncertainty bounds for the year 2009.
Figure 21.
FFCs at site 22, along with stationary uncertainty bounds for the year 1996.
Figure 21.
FFCs at site 22, along with stationary uncertainty bounds for the year 1996.
Figure 22.
Comparison between non-stationary and stationary FFCs at site 24, along with non-stationary uncertainty bounds for the year 2009.
Figure 22.
Comparison between non-stationary and stationary FFCs at site 24, along with non-stationary uncertainty bounds for the year 2009.
Table 1.
Basic information of flow gauges and sub-basins in the KRB, Pakistan.
Table 1.
Basic information of flow gauges and sub-basins in the KRB, Pakistan.
Site# | Sub Basin and Flow Gauge Stations | Basin Area (km2) | Coefficient of Variation (Cv) | Number of Years of Record |
---|
| Kabul River Basin | 87,499 | | |
1 | Kabul River at Warsak | | 0.292 | 52 (1965–2016) |
2 | Kabul River at Nowshera | 0.433 | 55 (1962–2016) |
3 | Shahalam River | 0.724 | 30 (1987–2016) |
4 | Naguman River | 0.829 | 30 (1987–2016) |
5 | Adezai River | 0.739 | 30 (1987–2016) |
| Chitral River Basin | 11,396 | | |
6 | Chitral River | | 0.2 | 50 (1964–2013) |
| Panjkora River Basin | 5917 | | |
7 | Panjkora River | | 0.859 | 33 (1984–2016) |
| Main Swat River Basin | 6066 | | |
8 | Swat River at Kalam | | 0.2 | 59 (1961–2009) |
9 | Swat River at Chakdara | 0.336 | 49 (1961–2009) |
10 | Swat River at Khawazakela | 0.84 | 34 (1983–2016) |
11 | Swat River at Ningolai | 1.425 | 31(1986–2016) |
| Lower Swat River Basin | 2685 | | |
12 | Swat River at Munda Head Works | | 0.744 | 55 (1962–2016) |
13 | Khiyali River at Charsada Road | 0.815 | 48 (1969–2016) |
14 | Jundi Nullah at Tangi | 3.06 | 37 (1974–2011) |
| Jindi River Basin | 13 | | |
15 | Jindi River | | 0.684 | 48 (1969–2016) |
| Kalpani River Basin | 2830 | | |
16 | Naranji Nullah | | 0.975 | 49 (1968–2016) |
17 | Badri Nullah | 0.893 | 45 (1966–2010) |
18 | Kalpani River at Mardan | 1.476 | 33 (1984–2016) |
19 | Kalpani River at Risalpur | 0.752 | 33 (1984–2016) |
20 | Dagi Nullah | 1.01 | 33 (1984–2016) |
21 | Bagiari Nullah | 0.917 | 30 (1987–2016) |
22 | Lund Khawar West | | 1.13 | 30 (1987–2016) |
| Bara River Basin | 3388 | | |
23 | Budni Nullah | | 1.28 | 43 (1974–2016) |
24 | Bara River at Kohat Bridge | 1.69 | 34 (1983–2016) |
25 | Khuderzai Nullah | 1.65 | 32 (1980–2011) |
26 | Chillah Nullah at Pabi | 1.15 | 32 (1980–2011) |
27 | Hakim Garhi Nullah | 0.6 | 31 (1980–2010) |
28 | Wazir Garhi Nullah | 1.69 | 30 (1981–2010) |
29 | Muqam Nullah | 0.781 | 30 (1981–2010) |
Table 2.
Description of trends in the annual maximum flood regime across the KRB, Pakistan.
Table 2.
Description of trends in the annual maximum flood regime across the KRB, Pakistan.
Site # | Mann–Kendall (Test-Z) | Site # | Mann–Kendall (Test-Z) | Site # | Mann–Kendall (Test-Z) |
---|
1 | −1.54 | 11 | 4.78 *** | 21 | 3.28 ** |
2 | −0.35 | 12 | −0.89 | 22 | 2.83 ** |
3 | 0.41 | 13 | 1.18 | 23 | −1.28 |
4 | −2.02 * | 14 | 0.86 | 24 | 2.28 * |
5 | 2.61 ** | 15 | −0.37 | 25 | −1.19 |
6 | 2.80 ** | 16 | 1.79 + | 26 | −0.67 |
7 | 0.93 | 17 | −3.07 ** | 27 | 0.34 |
8 | −1.36 | 18 | 3.24 ** | 28 | −0.54 |
9 | 1.73 + | 19 | 2.13 * | 29 | −0.83 |
10 | −2.36 * | 20 | 0.16 | | |
Table 3.
The goodness of fit statistics of annual maximum daily peak flow to generalized extreme value (GEV) distribution.
Table 3.
The goodness of fit statistics of annual maximum daily peak flow to generalized extreme value (GEV) distribution.
Site # | Gauge Stations | GEV Parameters | Anderson–Darling Test | Kolmogorov–Smirnov Test |
---|
A-D Statistics | K-S Statistics | p-Value |
---|
5 | Adezai River | ξ = 0.07899 σ = 454.66 µ = 521.18 | 0.6903 | 0.15394 | 0.43251 |
6 | Chitral River | ξ = 0.00307 σ = 143.37 µ = 1026.5 | 0.22503 | 0.06435 | 0.97732 |
9 | Swat River at Chakdara | ξ = 0.13247 σ = 152.1 µ = 646.8 | 0.66053 | 0.10305 | 0.59055 |
11 | Swat River at Ningolai | ξ = 0.52162 σ = 103.82 µ = 83.499 | 0.60066 | 0.1453 | 0.48501 |
16 | Naranji Nullah | ξ = 0.25789 σ = 77.168 µ = 81.939 | 0.19219 | 0.06263 | 0.98424 |
18 | Kalpani River at Mardan | ξ = 0.55205 σ = 106.9 µ = 77.204 | 1.2218 | 0.17818 | 0.21796 |
19 | Kalpani River at Risalpur | ξ = 0.20781 σ = 441.0 µ = 604.88 | 0.42201 | 0.10944 | 0.7987 |
21 | Bagiari Nullah | ξ = 0.06073 σ = 112.05 µ = 94.608 | 1.838 | 0.22761 | 0.08399 |
22 | Lund Khawar West | ξ = 0.37899 σ = 3.7993 µ = 3.164 | 0.48511 | 0.12903 | 0.7523 |
24 | Bara River at Kohat Bridge | ξ = 0.57308 σ = 16.871 µ = 9.4788 | 1.2595 | 0.15782 | 0.33006 |
Table 4.
Representation of detected outliers, as per Chauvenet’s criterion.
Table 4.
Representation of detected outliers, as per Chauvenet’s criterion.
Site # | Station Name | Historical Extreme (Outliers) | Observed Value | Critical Value |
---|
5 | Adezai River | 2285 | 2.449 | 2.394 |
6 | Chitral River | 1633/1603 | 2.941/2.76 | 2.576 |
9 | Swat River at Chakdara | 1918/1602 | 4.6/3.35 | 2.576 |
11 | Swat River at Ningolai | 1475 | 3.447 | 2.406 |
16 | Naranji Nullah | 850 | 4.748 | 2.576 |
18 | Kalpani River at Mardan | 1499 | 3.182 | 2.429 |
19 | Kalpani River at Risalpur | 3358 | 3.316 | 2.418 |
21 | Bagiari Nullah | 473 | 2.102 | 2.394 |
22 | Lund Khawar West | 37 | 3.235 | 2.394 |
24 | Bara River at Kohat Bridge | 331 | 4.234 | 2.44 |
Table 5.
Correlation matrix for the selected study sites.
Table 5.
Correlation matrix for the selected study sites.
Site # | 5 | 6 | 9 | 11 | 16 | 18 | 19 | 21 | 22 | 24 |
---|
5 | 1 | 0.24 | −0.04 | 0.63 | 0.35 | 0.61 | 0.14 | 0.25 | 0.39 | 0.48 |
6 | 0.24 | 1 | 0.29 | 0.11 | 0.42 | 0.33 | 0.42 | 0.37 | 0.38 | 0.41 |
9 | −0.04 | 0.29 | 1 | 0.11 | 0.11 | −0.05 | −0.22 | −0.02 | −0.17 | 0.04 |
11 | 0.63 | 0.11 | 0.11 | 1 | 0.2 | 0.59 | 0.04 | 0.49 | 0.6 | 0.21 |
16 | 0.35 | 0.42 | 0.12 | 0.2 | 1 | 0.41 | 0.47 | 0.29 | 0.32 | 0.63 |
18 | 0.61 | 0.33 | −0.05 | 0.59 | 0.41 | 1 | 0.63 | 0.53 | 0.52 | 0.54 |
19 | 0.14 | 0.42 | −0.22 | 0.04 | 0.47 | 0.63 | 1 | 0.65 | 0.64 | 0.42 |
21 | 0.25 | 0.37 | −0.02 | 0.49 | 0.29 | 0.53 | 0.65 | 1 | 0.41 | 0.2 |
22 | 0.39 | 0.38 | −0.17 | 0.6 | 0.32 | 0.52 | 0.64 | 0.41 | 1 | 0.47 |
24 | 0.48 | 0.41 | 0.04 | 0.21 | 0.63 | 0.54 | 0.42 | 0.2 | 0.47 | 1 |
Table 6.
Comparison between 100-year flood estimates using the stationary and non-stationary Bayesian models for “at site modeling” for the KRB, Pakistan.
Table 6.
Comparison between 100-year flood estimates using the stationary and non-stationary Bayesian models for “at site modeling” for the KRB, Pakistan.
Site # | Station Name | Historical Extreme m3 s−1 | Stationary m3 s−1 | Non-Stationary m3 s−1 | Difference b/w Stationary & Non-Stationary m3 s−1 | Percent Difference (%) | Bayes Factor | % Difference between Preferred Model and Historical Extreme |
---|
5 | Adezai River | 2285 | 4276 | 2782 | 1494 | 34.9 | 0.0058 | 17.86 |
6 | Chitral River | 1633 | 1895 | 1918 | −23 | −1.19 | 0.068 | 14.85 |
9 | Swat River at Chakdara | 1918 | 1991 | 2686 | −695 | −25.8 | 7.06 | 3.8 |
11 | Swat River at Ningolai | 1475 | 2891 | 2528 | 363 | 12.5 | 0.0065 | 41.65 |
16 | Naranji Nullah | 850 | 1127 | 1222 | −95 | −7.7 | 9.55 | 24.6 |
18 | Kalpani River at Mardan | 1499 | 3881 | 2887 | 1054 | 27.15 | −Infinity | 48.14 |
19 | Kalpani River at Risalpur | 3358 | 4918 | 5140 | −222 | −4.31 | 0.4348 | 34.66 |
21 | Bagiari Nullah | 473 | 1666 | 819 | 847 | 50.8 | 0.0321 | 42.24 |
22 | Lund Khawar West | 37 | 76 | 51 | 25 | 32.89 | 0.11 | 27.45 |
24 | Bara River at Kohat Bridge | 331 | 686.7 | 357.5 | 330.9 | 48.18 | −Infinity | 7.2 |
Table 7.
Performance of Bayesian models for predicting the extreme floods in the KRB, Pakistan.
Table 7.
Performance of Bayesian models for predicting the extreme floods in the KRB, Pakistan.
Site # | Time Series Length | Extreme Event (Year) | Mann–Kendall (Test-Z) | Stationary m3 s−1 | Non-Stationary m3 s−1 | Difference between Stationary and Non-Stationary m3 s−1 | Percent Difference (%) | Bayes Factor |
---|
5 | 1987–2009 | 2010 | −0.05 | 3300 | N/A | N/A | N/A | N/A |
6 | 1964–2004 | 2005/2010 | 2.88 ** | 1701 | 1978 | 277 | 14 | 0.0054 |
9 | 1961–1991 | 1992 | 1.42 | 1746 | N/A | N/A | N/A | N/A |
11 | 1986–2015 | 2016 | 4.49 *** | 2211 | 1295 | 916 | 41.43 | 15.167 |
16 | 1968–2009 | 2010 | 1.31 | 850.8 | N/A | N/A | N/A | N/A |
18 | 1984–2009 | 2010 | 2.29 * | 1472 | 1085 | 387 | 26.3 | 0.1208 |
19 | 1984–2009 | 2010 | 2.76 ** | 4580 | 3595 | 990 | 21.6 | 0.008 |
21 | 1987–2009 | 2010 | 2.2 * | 1469 | 704 | 765 | 52 | 0.016 |
22 | 1987–1996 | 1997 | −0.28 | 30.38 | N/A | N/A | N/A | N/A |
24 | 1983–2009 | 2010 | 1.15 | 339.6 | 355 | 15.4 | 4.33 | +Infinity |