Daily annual maximum wind speed values are among environmental events with the most catastrophic consequences for society. A comprehensive understanding of the magnitudes and frequency of extreme winds is essential for ensuring sustainably managed wind energy, planning for emergency weather situations, and designing different building structures. This study investigated regional frequency analysis of daily annual maximum winds for Baluchistan and Sindh provinces of Pakistan. We intended to find the regional frequency distribution for maximum winds and predict the returns for extreme winds events in the future. L-moments regionalization techniques along with flood index procedure were applied to maximum wind speed records of 21 stations across the study area. Only one station namely Lasbella was found to be discordant. With the help of cluster analysis, the remaining twenty stations were further divided into two homogeneous. Heterogeneity measures validate that both regions are homogenous with allotted stations. Regional quantiles for both regions are estimated through best-fit probability distribution among Generalized Normal (GNO), Generalized Logistic (GLO), Pearson Type 3 (P3), Generalized Pareto (GPA), and Generalized Extreme Value (GEV). Robustness of GLO distribution compared to GEV distribution is assessed through Monte Carlo simulations of relative bias and relative root mean square error. Findings clearly show that GLO distribution is best for the regional modeling. Furthermore, at-site quantiles are estimated by multiplying quantities of regional quantiles using the sample mean and median as scaling factors. Estimated quantiles can be helpful for future planning concerning wind energy and the codification of structural designs and policy implications.
Research Article
An estimation of regional and at-site quantiles of extreme winds under flood index procedure
https://doi.org/10.21203/rs.3.rs-1668488/v1
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Linear-moments
Monte Carlo simulation
Quantile estimates
Wind speed
Regional frequency analysis
Table 1
Observed stations information and their exploratory analysis.
|
Station |
Name |
Latitude |
Longitude |
Elevation |
Mean |
SD |
CV |
Skewness |
Kurtosis |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 |
Chhor Hydrabad Jiwani Jacobabad Karachi.A.P Nawabshah Punjgur Pasni Badin Gwadar Larkana Padidan Rohri Ormara Turbat Karachi Dadu Mirpurkhas Thatta Uthal Lasbella |
29.53 25.23 25.04 28.18 24.54 26.15 26.58 25.16 24.38 25.08 27.32 26.51 27.40 25.12 25.59 24.54 26.43 25.31 24.45 25.49 25.84 |
69.43 68.25 61.48 68.28 67.08 68.22 64.04 63.29 68.54 62.20 68.14 68.08 68.54 64.40 63.04 66.56 67.47 69.00 67.54 66.37 66.52 |
1046.90 53.86 30.69 69.51 48.58 59.83 1037.86 54.34 5.32 49.08 51.26 45.41 59.87 94.54 254.44 24.28 357.64 17.20 5.97 40.43 68.25 |
10.77 12.39 12.11 10.76 12.18 11.83 15.87 13.78 12.79 12.03 11.37 11.54 11.75 13.52 16.48 12.04 12.07 12.29 12.37 12.29 11.96 |
1.10 0.97 0.85 1.02 1.16 1.00 1.60 1.15 1.00 0.85 0.89 0.92 0.98 1.46 1.31 1.65 1.24 1.04 1.40 2.03 1.68 |
0.06 0.05 0.08 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.05 0.05 0.05 0.05 0.04 0.07 0.06 0.05 0.06 0.07 0.05 |
0.02 -0.02 0.11 0.15 0.17 0.04 0.24 0.19 0.06 0.24 -0.01 0.07 -0.12 0.33 0.17 0.25 0.10 0.08 0.24 0.33 0.34 |
0.16 0.12 0.09 0.23 0.22 0.15 0.28 0.19 0.04 0.19 0.12 0.14 0.09 0.25 0.14 0.32 0.18 0.23 0.20 0.35 0.19 |
Table 2
The results of basic assumptions and p-value is given in parenthesis
|
Station |
location |
Wald-Wolfowitz Test |
Mann-Whitney test |
Spearman Rank Correlation test |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 |
Chhor Hydrabad Jiwani Jacobabad Karachi.A.P Nawabshah Punjgur Pasni Badin Gwadar Larkana Padidan Rohri Ormara Turbat Karachi Dadu Mirpurkhas Thatta Uthal Lasbella |
0.72 (0.24) 0.20 (0.43) -0.36 (0.36) -0.57 (0.28) -0.28 (0.39) 0.28 (0.39) -0.50 (0.31) -1.47 (0.11) 0.46 (0.32) 0.23 (0.41) -0.63 (0.27) 0.84 (0.20) 1.23 (0.11) -0.44 (0.33) 0.49 (0.31) -0.99 (0.16) -0.53 (0.30) -0.66 (0.26) -0.18 (0.43) -0.43 (0.33) -0.64 (0.24) |
-0.89 (0.19) -1.64 (0.05) -1.43 (0.08) -0.15 (0.44) -0.10 (0.46) -1.64 (0.05) -1.63 (0.05) -1.47 (0.07) -1.55 (0.06) -0.08 (0.21) -1.14 (0.13) -1.22 (0.11) -0.52 (0.30) -0.60 (0.27) -1.40 (0.08) -0.81 (0.21) -1.56 (0.06) -0.97 (0.17) -1.56 (0.06) -2.26 (0.06) -1.42(0.08) |
-0.62 (0.27) -0.61 (0.27) -1.74 (0.04) 1.19 (0.12) 0.80 (0.21) 0.09 (0.46) -1.71 (0.10) 1.55 (0.06) -1.59 (0.06) -0.58 (0.28) -0.43 (0.34) 0.19 (0.44) 0.05 (0.48) -0.85 (0.20) 1.90 (0.03) -1.13 (0.13) -0.55 (0.29) -0.26 (0.40) -1.57(0.06) -1.95 (0.07) -1.04 (0.09) |
Table 3
L-Moments and Discordancy Measure.
Table 5
LMs and Discordancy Measure corresponding to Region I and Region-II.
Table 6
Heterogeneity Statistic for Homogeneous Region-I and Region-II.
|
Region I |
|
|
|
Heterogeneity measure Heterogeneity measureHeterogeneity measure |
0.31 -0.22
-0.18 |
|
|
Region II |
||
|
Heterogeneity measure Heterogeneity measureHeterogeneity measure |
-0.78 -0.48
-1.23 |
|
Table 7
Goodness of fit of the model for homogenous Region I and Region II
|
Region |
ZGLO | ZGLO| |
ZGEV |ZGEV| |
ZGNO | ZGNO| |
ZPE3 | ZPE3| |
ZGPA | ZGPA| |
|
1
2
|
-0.85 0.85* -0.62 0.62* |
-2.43 2.43 -1.49 1.49 |
-2.71 2.71 -1.07 1.07 |
-3.35 3.35 -1.09 1.09 |
-6.02 6.02 -5.45 5.45 |
*Indicate the best fit distribution.
Table 8
Regional based parameters and quantile of best fitted distribution.
Table 9
At site Quantile Estimate corresponding 2-, 5-, 10-, 20-, 50-, 100-, 500-, and 1000- years return periods at Region I using mean and [median] as scaling factors.
|
Badin
Mirpurkhas
Hydrabad
Thatta
KarachiA.P
Uthal
Karachi
Punjgur
Turbat
Ormara
Pasni
Gwadar
Jiwani
|
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO |
12.59 [12.44] 12.10 [12.16] 12.20 [12.16] 12.18 [12.71] 12.00 [11.93] 12.10 [11.91] 11.86 [11.58] 15.63 [15.22] 16.24 [16.16] 13.32 [13.08] 13.57 [13.52] 11.85 [11.58] 11.93 [11.82] |
13.56 [13.38`] 13.03 [13.09] 13.14 [13.10] 13.12 [12.60] 12.92 [12.85] 13.03 [12.83] 12.76 [12.47] 16.83 [16.39] 17.48 [17.40] 14.34 [14.08] 14.61 [14.56] 12.76 [12.47] 12.85 [12.73] |
14.25 [14.07] 13.69 [13.76] 13.81 [13.76] 13.78 [13.24] 13.58 [13.50] 13.70 [13.48] 13.41 [13.11] 17.68 [17.22] 18.37 [18.28] 15.07 [14.79] 15.35 [15.30] 13.40 [13.11] 13.50 [13.72] |
14.98 [14.79] 14.39 [14.47] 14.52 [14.47] 14.49 [13.93] 14.27 [14.20] 14.40 [14.17] 14.11 [14.78] 18.59 [18.11] 19.32 [19.22] 15.84 [15.56] 16.14 [16.09] 14.09 [13.78] 14.19 [14.06] |
16.07 [15.87] 15.45 [15.52] 15.57 [15.52] 15.55 [14.94] 15.31 [15.23] 15.45 [15.20] 15.13 [14.78] 19.94 [19.43] 20.72 [20.62] 16.99 [16.69] 17.32 [17.26] 15.12 [14.78] 15.23 [15.08] |
17.01 [16.80] 16.35 [14.43] 16.49 [16.43] 16.46 [15.81] 16.21 [16.12] 16.35 [16.09] 16.02 [16.65] 21.11 [20.56] 21.93 [21.83] 17.97 [17.66] 18.33 [18.27] 16.00 [15.65] 16.12 [15.97] |
19.70 [19.45] 18.93 [19.02] 19.09 [19.03] 19.06 [18.31] 18.77 [18.66] 18.93 [18.63] 18.54 [18.12] 24.45 [23.81] 25.40 [25.27] 20.83 [20.45] 21.23 [21.15] 18.53 [18.12] 18.66 [18.49] |
21.12 [20.86] 20.30 [20.39] 20.47 [20.40] 20.43 [19.63] 20.12 [20.01] 20.30 [19.98] 19.88 [19.43] 26.21 [25.53] 27.23 [27.10] 22.33 [21.93] 22.76 [22.68] 19.87 [19.43] 20.01 [19.82] |
Table 10
At site Quantile Estimate corresponding 2-, 5-, 10-, 20-, 50-, 100-, 500-, and 1000- years return periods at Region II using mean and [median] as scaling factors.
|
Site Name |
Dist. |
2 |
5 |
10 |
20 |
50 |
100 |
500 |
1000 |
|
Nawabshah
Padidan
Larkana
Rohri
Jacobabad
Dadu
Chhor
|
GLO
GLO
GLO
GLO
GLO
GLO
GLO |
11.79 [11.79] 11.51 [11.29] 11.34 [11.27] 11.71 [11.69] 10.72 [10.52] 12.03 [12.02] 10.73 [10.65] |
12.65 [12.65] 12.34 [12.11] 12.16 [12.09] 12.56 [12.53] 11.41 [11.28] 12.90 [12.89] 11.51 [11.42] |
13.17 [13.16] 12.84 [12.60] 12.66 [12.59] 13.07 [13.05] 11.97 [11.74] 13.43 [13.41] 11.98 [11.89] |
13.66 [13.66] 13.33 [13.07] 13.13 [13.06] 13.56 [13.54] 12.42 [12.18] 13.93 [13.92] 12.43 [12.34] |
14.30 [14.30] 13.95 [13.69] 13.75 [13.67] 14.20 [14.18] 13.00 [12.76] 14.59 [14.57] 13.02 [12.92] |
14.80 [14.80] 14.44 [14.17] 14.23 [14.15] 14.69 [14.67] 13.45 [13.20] 15.09 [15.08] 13.47 [13.37] |
15.99 [15.99] 15.60 [15.30] 15.37 [15.28] 15.87 [15.84] 14.53 [14.26] 16.31 [16.29] 14.55 [14.44] |
16.52 [16.52] 16.12 [16.81] 15.88 [16.79] 16.40 [14.37] 15.02 [16.73] 16.85 [16.83] 15.03 [14.92] |
Table 11
Standard errors of at-site quantile estimates of region I using mean and [median] as scaling factor.
|
Site Name |
Dist. |
Q2 |
Q5 |
Q10 |
Q20 |
Q50 |
Q100 |
Q500 |
Q1000 |
|
Badin
Mirpurkhas
Hyderabad
Thatta
KarachiA.P
Uthal
Karachi
Punjgur
Turbat
Ormara
Pasni
Gwadar
Jiwani
|
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO
GLO |
0.91 [0.91] 0.88 [0.90] 0.88 [0.89] 0.90 [0.96] 0.88 [0.89] 0.93 [0.96] 0.89 [0.91] 1.15 [1.14] 1.18 [1.18] 0.98 [0.99] 0.96 [1.00] 0.86 [0.85] 0.86 [0.86] |
1.46 [1.45] 1.40 [1.42] 1.41 [1.41] 1.42 [1.39] 1.39 [1.40] 1.44 [1.45] 1.39 [1.39] 1.82 [1.79] 1.88 [1.88] 1.55 [1.54] 1.57 [1.57] 1.37 [1.35] 1.38 [1.37] |
1.96 [1.94] 1.89 [1.90] 1.90 [1.90] 1.91 [1.85] 1.87 [1.87] 1.92 [1.92] 1.87 [1.84] 2.44 [2.39] 2.53 [2.52] 2.08 [2.06] 2.11 [2.11] 1.84 [1.81] 1.85 [1.84] |
2.36 [2.34] 2.27 [2.29] 2.29 [2.29] 2.30 [2.22] 2.26 [2.25] 2.30 [2.29] 2.24 [2.21] 2.94 [2.88] 3.05 [3.04] 2.51 [2.48] 2.55 [2.55] 2.22 [2.18] 2.24 [2.22] |
2.83 [2.81] 2.73 [2.74] 2.75 [2.74] 2.75 [2.66] 2.71 [2.70] 2.76 [2.74] 2.69 [2.64] 3.53 [3.45] 3.66 [3.65] 3.01 [2.96] 3.06 [3.05] 2.67 [2.61] 2.68 [2.66] |
3.17 [3.13] 3.05 [3.07] 3.07 [3.07] 3.07 [3.97] 3.02 [3.01] 3.08 [3.05] 3.00 [2.95] 3.94 [3.85] 4.08 [4.07] 3.36 [3.31] 3.42 [3.41] 2.98 [2.92] 3.00 [2.98] |
3.91 [3.87] 3.76 [3.78] 3.79 [3.78] 3.79 [3.66] 3.73 [3.72] 3.79 [3.76] 3.70 [3.63] 4.86 [4.75] 5.04 [5.02] 4.14 [4.08 4.21] [4.21] 3.67 [3.60] 3.70 [3.67] |
4.22 [4.17] 4.06 [4.08] 4.09 [4.08] 4.09 [3.95] 4.03 [4.01] 4.09 [4.06] 3.99 [3.92] 5.25 [5.13] 5.44 [5.42] 4.47 [4.41] 4.55 [4.54] 3.97 [3.89] 4.00 [3.96] |
Table 12
Standard errors of at-site quantile estimates of region II using mean and [median] as scaling factor.
|
Site Name |
Dist |
Q2 |
Q5 |
Q10 |
Q20 |
Q50 |
Q100 |
Q500 |
Q1000 |
|
Nawabshah
Padidan
Larkana
Rohri
Jacobabad
Dadu
Chhor
|
GLO
GLO
GLO
GLO
GLO
GLO
GLO |
0.73 [0.74] 0.71 [0.71] 0.70 [0.71] 0.72 [0.74] 0.67 [0.67] 0.76 [0.77] 0.67 [0.67] |
0.98 [0.99] 0.95 [0.94] 0.94 [0.94] 0.97 [0.98] 0.89 [0.89] 1.00 [1.02] 0.90 [0.91] |
1.22 [1.23] 1.19 [1.17] 1.17 [1.17] 1.21 [1.22] 1.11 [1.10] 1.25 [1.26] 1.12 [1.12] |
1.44 [1.45] 1.41 [1.39] 1.39 [1.39] 1.43 [1.44] 1.32 [1.30] 1.48 [1.49] 132 [132] |
1.74 [1.74] 1.69 [1.67] 1.67 [1.66] 1.72 [1.73] 1.58 [1.56] 1.78 [1.79] 1.59 [1.58] |
1.95 [1.96] 1.90 [1.88] 1.88 [1.88] 1.94 [1.94] 1.78 [1.76] 2.00 [2.01] 1.78 [1.78] |
2.46 [2.47] 2.40 [2.37] 2.37 [2.36] 2.45 [2.45] 2.24 [2.21] 2.52 [2.53] 2.25 [2.24] |
2.69 [2.69] 2.62 [2.58] 2.58 [2.57] 2.67 [2.67] 2.45 [2.41] 2.75 [2.75] 2.45 [2.44] |
No competing interests reported.