Abstract
The frequency of extreme rainfall occurrence is expected to increase in the future and neglecting these changes will result in the underestimation of extreme events. Nonstationary extreme value modelling is one of the ways to incorporate changing conditions into analyses. Although the definition of nonstationary is still debated, the existence of nonstationarity is determined by the presence of significant monotonic upward or downward trends and/or shifts in the mean or variance. On the other hand, trend tests may not be a sign of nonstationarity and a lack of significant trend cannot be accepted as time series being stationary. Thus, this study investigated the relation between trend and nonstationarity for 5, 10, 15, and 30 min and 1, 3, 6, and 24 h annual maximum rainfall series at 13 stations in Central Anatolia, Turkey. Trend tests such as Mann–Kendall (MK), Cox–Stuart (CS), and Pettitt’s (P) tests were applied and nonstationary generalized extreme value models were generated. MK test and CS test results showed that 33% and 27% of 104 time series indicate a significant trend (with p < 0.01–p < 0.05–p < 0.1 significance level), respectively. Moreover, 43% of time series have outperformed nonstationary (NST) models that used time as covariate. Among five different time-variant nonstationary models, the model with a location parameter as a linear function of time and the model with a location and scale parameter as a linear function of time performed better. Considering the rainfall series with a significant trend, increasing trend power may increase how well fitted nonstationary models are. However, it is not necessary to have a significant trend to obtain outperforming nonstationary models. This study supported that it is not necessarily time series to have a trend to perform better nonstationary models and acceptance of nonstationarity solely depending on the presence of trend may be misleading.
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Appendix
Appendix
Model | 5 min | 10 min | 15 min | 30 min | 1 h | 3 h | 6 h | 24 h | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | AIC | BIC | |
Aksaray | ||||||||||||||||
NST1 | 250.23 | 259.88 | 272.38 | 282.04 | 303.64 | 313.30 | 319.11 | 328.77 | 346.32 | 355.97 | 353.02 | 362.68 | ||||
NST2 | 201.61 | 211.27 | 249.55 | 259.21 | 272.74 | 282.40 | 302.45 | 312.11 | 316.45 | 326.11 | 344.16 | 353.82 | 352.13 | 361.79 | 369.35 | 379.01 |
NST3 | 199.96 | 207.69 | 247.67 | 255.40 | 270.71 | 278.43 | 300.62 | 308.35 | 316.82 | 324.55 | 346.56 | 354.28 | 356.67 | 364.39 | 368.35 | 376.07 |
NST4 | 248.40 | 256.12 | 271.94 | 279.67 | 301.77 | 309.50 | 317.28 | 325.01 | 345.72 | 353.45 | 367.34 | 375.07 | ||||
NST5 | 199.56 | 207.29 | 248.41 | 256.14 | 272.00 | 279.73 | 301.85 | 309.58 | 317.29 | 325.01 | 345.85 | 353.58 | 352.19 | 359.92 | 367.41 | 375.13 |
ST | 198.08 | 203.88 | 246.52 | 252.32 | 270.43 | 276.22 | 300.48 | 306.28 | 315.32 | 321.11 | 344.75 | 350.55 | 354.69 | 360.48 | 366.35 | 372.14 |
Ankara | ||||||||||||||||
NST1 | 320.53 | 331.48 | 397.11 | 408.06 | 429.25 | 440.20 | 452.82 | 463.77 | 471.64 | 482.59 | 484.15 | 495.10 | 510.95 | 521.90 | ||
NST2 | 368.04 | 378.99 | 394.97 | 405.92 | 426.53 | 437.48 | 449.84 | 460.79 | 471.42 | 482.36 | 484.14 | 495.09 | 510.46 | 521.41 | ||
NST3 | 321.35 | 330.11 | 369.30 | 378.06 | 394.74 | 403.50 | 426.61 | 435.37 | 452.34 | 461.10 | 469.85 | 478.60 | 482.28 | 491.04 | 510.83 | 519.59 |
NST4 | 327.75 | 336.51 | 395.88 | 404.64 | 427.42 | 436.18 | 450.89 | 459.64 | 469.65 | 478.40 | 482.15 | 490.91 | 508.97 | 517.73 | ||
NST5 | 327.79 | 336.55 | 370.71 | 379.47 | 395.87 | 404.63 | 427.43 | 436.19 | 450.98 | 459.74 | 469.66 | 478.42 | 482.26 | 491.01 | 508.95 | 517.71 |
ST | 326.52 | 333.09 | 369.21 | 375.78 | 394.06 | 400.63 | 425.57 | 432.13 | 450.55 | 457.12 | 467.86 | 474.43 | 480.28 | 486.85 | 511.34 | 517.91 |
Çankırı | ||||||||||||||||
NST1 | 284.02 | 294.24 | 320.44 | 330.65 | 345.02 | 355.23 | 383.20 | 393.41 | 391.97 | 402.19 | 419.32 | 429.54 | ||||
NST2 | 283.80 | 294.02 | 319.97 | 330.19 | 344.99 | 355.21 | 375.50 | 385.72 | 382.52 | 392.74 | 390.07 | 400.28 | 391.28 | 401.49 | 418.56 | 428.78 |
NST3 | 281.93 | 290.11 | 317.98 | 326.16 | 343.03 | 351.20 | 374.53 | 382.71 | 383.12 | 391.30 | 388.14 | 396.32 | 390.84 | 399.01 | 417.37 | 425.55 |
NST4 | 284.42 | 292.59 | 318.83 | 327.00 | 343.02 | 351.19 | 382.06 | 390.23 | 395.56 | 403.73 | 418.39 | 426.56 | ||||
NST5 | 284.42 | 292.59 | 318.83 | 327.00 | 343.02 | 351.19 | 374.34 | 382.51 | 381.99 | 390.16 | 390.86 | 399.03 | 395.57 | 403.74 | 419.71 | 427.88 |
ST | 282.42 | 288.55 | 316.83 | 322.96 | 341.04 | 347.17 | 372.59 | 378.72 | 381.00 | 387.13 | 389.55 | 395.68 | 396.58 | 402.71 | 418.59 | 424.72 |
Eskişehir | ||||||||||||||||
NST1 | 291.54 | 301.67 | 332.26 | 342.39 | 359.77 | 369.90 | 400.44 | 410.57 | 411.48 | 421.60 | ||||||
NST2 | 290.38 | 300.51 | 331.08 | 341.20 | 358.73 | 368.86 | 400.23 | 410.35 | 411.37 | 421.50 | 400.09 | 410.21 | 401.75 | 411.87 | 402.76 | 412.89 |
NST3 | 288.49 | 296.59 | 330.50 | 338.61 | 358.35 | 366.45 | 399.95 | 408.05 | 410.02 | 418.13 | 398.29 | 406.39 | 400.99 | 409.09 | 405.15 | 413.25 |
NST4 | 290.58 | 298.68 | 330.37 | 338.48 | 357.85 | 365.95 | 398.45 | 406.55 | 409.48 | 417.58 | ||||||
NST5 | 290.58 | 298.68 | 330.29 | 338.39 | 357.79 | 365.90 | 398.34 | 406.44 | 409.56 | 417.66 | 398.61 | 406.71 | 401.30 | 409.40 | 402.53 | 410.63 |
ST | 288.66 | 294.74 | 330.00 | 336.08 | 357.88 | 363.96 | 398.00 | 404.08 | 408.02 | 414.10 | 396.65 | 402.73 | 399.44 | 405.51 | 403.16 | 409.24 |
Karaman | ||||||||||||||||
NST1 | 252.61 | 262.27 | 289.45 | 299.11 | 304.71 | 314.37 | 325.16 | 334.82 | 330.95 | 340.61 | 361.70 | 371.36 | 383.18 | 392.84 | ||
NST2 | 252.49 | 262.15 | 289.39 | 299.05 | 304.56 | 314.22 | 324.30 | 333.95 | 330.30 | 339.96 | 350.73 | 360.39 | 361.61 | 371.27 | 382.23 | 391.89 |
NST3 | 250.98 | 258.70 | 287.40 | 295.13 | 302.73 | 310.45 | 323.48 | 331.21 | 330.58 | 338.30 | 348.86 | 356.59 | 359.65 | 367.38 | 380.73 | 388.46 |
NST4 | 250.93 | 258.65 | 287.53 | 295.26 | 303.38 | 311.11 | 324.67 | 332.40 | 331.06 | 338.79 | 359.72 | 367.45 | 381.20 | 388.93 | ||
NST5 | 250.91 | 258.63 | 287.52 | 295.24 | 303.38 | 311.11 | 324.70 | 332.43 | 331.04 | 338.77 | 348.89 | 356.62 | 359.72 | 367.45 | 381.24 | 388.96 |
ST | 249.05 | 254.84 | 285.67 | 291.47 | 301.42 | 307.22 | 322.72 | 328.52 | 329.18 | 334.98 | 346.89 | 352.69 | 357.72 | 363.52 | 379.32 | 385.11 |
Kayseri | ||||||||||||||||
NST1 | 281.40 | 291.95 | 338.33 | 348.88 | 391.36 | 401.91 | 414.14 | 424.69 | 423.74 | 434.30 | 429.66 | 440.22 | ||||
NST2 | 281.36 | 291.92 | 336.95 | 347.51 | 354.01 | 364.57 | 389.34 | 399.89 | 412.89 | 423.44 | 421.37 | 431.93 | 427.90 | 438.46 | 436.71 | 447.26 |
NST3 | 280.40 | 288.84 | 335.02 | 343.47 | 352.04 | 360.49 | 388.17 | 396.62 | 411.89 | 420.34 | 419.69 | 428.14 | 426.40 | 434.85 | 432.27 | 440.71 |
NST4 | 283.43 | 291.87 | 339.44 | 347.89 | 354.90 | 363.35 | 391.40 | 399.84 | 413.85 | 422.29 | 422.69 | 431.14 | 428.01 | 436.45 | 434.55 | 442.99 |
NST5 | 283.43 | 291.88 | 339.51 | 347.95 | 354.95 | 363.40 | 391.71 | 400.16 | 413.95 | 422.40 | 422.95 | 431.39 | 428.08 | 436.52 | 434.60 | 443.04 |
ST | 281.49 | 287.82 | 338.26 | 344.59 | 353.29 | 359.62 | 391.10 | 397.43 | 412.74 | 419.07 | 423.07 | 429.40 | 426.08 | 432.41 | 432.71 | 439.04 |
Kırıkkale | ||||||||||||||||
NST1 | 252.57 | 262.03 | 301.81 | 311.27 | 324.05 | 333.51 | 345.89 | 355.35 | 352.45 | 361.91 | 353.38 | 362.84 | 357.88 | 367.34 | ||
NST2 | 281.36 | 291.92 | 301.80 | 311.26 | 324.00 | 333.46 | 345.63 | 355.08 | 352.37 | 361.83 | 353.29 | 362.75 | 357.92 | 367.38 | 367.61 | 377.07 |
NST3 | 250.61 | 258.18 | 299.85 | 307.42 | 322.46 | 330.02 | 344.44 | 352.01 | 350.86 | 358.43 | 351.32 | 358.89 | 356.10 | 363.67 | 365.63 | 373.20 |
NST4 | 250.91 | 258.48 | 299.99 | 307.56 | 322.04 | 329.61 | 344.04 | 351.60 | 350.46 | 358.03 | 351.43 | 359.00 | 355.87 | 363.44 | 364.85 | 372.42 |
NST5 | 250.92 | 258.48 | 299.99 | 307.56 | 322.10 | 329.67 | 344.43 | 351.99 | 350.90 | 358.46 | 351.45 | 359.02 | 355.90 | 363.46 | 365.62 | 373.18 |
ST | 248.92 | 254.59 | 297.99 | 303.67 | 320.49 | 326.16 | 342.44 | 348.11 | 348.92 | 354.59 | 349.65 | 355.33 | 354.11 | 359.78 | 363.63 | 369.31 |
Kırşehir | ||||||||||||||||
NST1 | 350.10 | 361.62 | 403.12 | 414.64 | 442.87 | 454.39 | 480.05 | 491.57 | 498.89 | 510.41 | 503.44 | 514.96 | 515.79 | 527.31 | 527.23 | 538.75 |
NST2 | 349.73 | 361.25 | 403.04 | 414.56 | 440.16 | 451.68 | 475.22 | 486.74 | 494.47 | 505.99 | 502.64 | 514.16 | 509.90 | 521.42 | 522.67 | 534.19 |
NST3 | 348.05 | 357.27 | 401.30 | 410.51 | 438.19 | 447.40 | 473.39 | 482.60 | 493.64 | 502.86 | 502.34 | 511.56 | 510.28 | 519.50 | 522.43 | 531.64 |
NST4 | 348.44 | 357.65 | 402.32 | 411.53 | 441.37 | 450.59 | 481.08 | 490.29 | 502.23 | 511.45 | 510.41 | 519.62 | 520.24 | 529.46 | 530.98 | 540.19 |
NST5 | 348.34 | 357.55 | 402.20 | 411.41 | 441.34 | 450.56 | 481.06 | 490.28 | 502.24 | 511.46 | 510.49 | 519.71 | 520.42 | 529.64 | 531.01 | 540.22 |
ST | 347.74 | 354.65 | 401.41 | 408.33 | 439.71 | 446.62 | 479.34 | 486.26 | 500.29 | 507.21 | 509.98 | 516.89 | 520.93 | 527.84 | 529.02 | 535.93 |
Konya | ||||||||||||||||
NST1 | 310.42 | 321.37 | 350.40 | 361.34 | 396.52 | 407.47 | 413.42 | 424.37 | 427.01 | 437.96 | 445.75 | 456.69 | ||||
NST2 | 310.48 | 321.43 | 350.38 | 361.33 | 373.10 | 384.05 | 396.18 | 407.13 | 413.34 | 424.29 | 425.80 | 436.75 | 444.20 | 455.15 | 489.98 | 500.92 |
NST3 | 308.99 | 317.75 | 348.50 | 357.26 | 370.93 | 379.68 | 394.29 | 403.05 | 411.90 | 420.66 | 424.08 | 432.84 | 442.13 | 450.89 | 493.21 | 501.97 |
NST4 | 308.85 | 317.61 | 348.40 | 357.16 | 370.79 | 379.55 | 394.66 | 403.42 | 411.98 | 420.74 | 425.08 | 433.84 | 444.51 | 453.26 | 494.70 | 503.46 |
NST5 | 308.86 | 317.62 | 348.40 | 357.16 | 370.80 | 379.56 | 394.66 | 403.42 | 411.97 | 420.73 | 425.10 | 433.86 | 444.91 | 453.67 | 495.32 | 504.07 |
ST | 307.21 | 313.78 | 346.50 | 353.07 | 369.10 | 375.67 | 392.67 | 399.24 | 410.18 | 416.75 | 423.25 | 429.81 | 443.45 | 450.02 | 493.37 | 499.94 |
Nevşehir | ||||||||||||||||
NST1 | 216.83 | 226.49 | 255.70 | 265.36 | 277.57 | 287.23 | 301.62 | 311.28 | 323.23 | 332.88 | 333.03 | 342.69 | 344.54 | 354.20 | 358.88 | 368.54 |
NST2 | 216.31 | 225.97 | 255.66 | 265.32 | 277.56 | 287.21 | 301.41 | 311.07 | 323.02 | 332.68 | 332.82 | 342.48 | 344.40 | 354.06 | 358.83 | 368.49 |
NST3 | 214.43 | 222.16 | 253.69 | 261.42 | 275.66 | 283.38 | 299.55 | 307.28 | 323.12 | 330.85 | 333.29 | 341.02 | 342.56 | 350.28 | 358.30 | 366.03 |
NST4 | 215.15 | 222.88 | 253.76 | 261.49 | 275.59 | 283.32 | 299.78 | 307.50 | 321.96 | 329.68 | 331.05 | 338.78 | 342.60 | 350.33 | 356.88 | 364.60 |
NST5 | 215.16 | 222.88 | 253.76 | 261.49 | 275.58 | 283.31 | 299.78 | 307.51 | 322.28 | 330.00 | 330.96 | 338.69 | 342.64 | 350.37 | 357.06 | 364.79 |
ST | 213.32 | 219.11 | 251.78 | 257.57 | 273.67 | 279.46 | 297.83 | 303.63 | 321.27 | 327.07 | 331.37 | 337.16 | 340.64 | 346.44 | 356.37 | 362.16 |
Niğde | ||||||||||||||||
NST1 | 235.54 | 245.76 | 267.64 | 277.85 | 285.65 | 295.87 | 318.36 | 328.57 | 332.37 | 342.58 | 378.64 | 388.86 | ||||
NST2 | 235.10 | 245.31 | 266.65 | 276.86 | 283.02 | 293.24 | 317.30 | 327.51 | 329.55 | 339.77 | 360.93 | 371.14 | 375.95 | 386.17 | 406.80 | 417.02 |
NST3 | 233.10 | 241.27 | 264.65 | 272.82 | 281.20 | 289.38 | 315.95 | 324.12 | 328.85 | 337.02 | 360.04 | 368.21 | 374.39 | 382.56 | 404.96 | 413.13 |
NST4 | 234.47 | 242.64 | 267.91 | 276.08 | 288.01 | 296.18 | 328.86 | 337.03 | 343.28 | 351.45 | 366.84 | 375.02 | 380.32 | 388.50 | ||
NST5 | 267.84 | 276.01 | 287.96 | 296.13 | 328.90 | 337.07 | 343.57 | 351.74 | 366.86 | 375.03 | 380.52 | 388.69 | 408.26 | 416.43 | ||
ST | 232.93 | 239.06 | 266.80 | 272.93 | 286.89 | 293.02 | 327.49 | 333.62 | 342.56 | 348.69 | 365.02 | 371.15 | 380.64 | 386.77 | 406.28 | 412.41 |
Sivas | ||||||||||||||||
NST1 | 267.92 | 278.23 | 293.00 | 303.30 | 316.96 | 327.26 | 343.33 | 353.63 | 368.50 | 378.80 | 372.38 | 382.68 | 404.11 | 414.42 | ||
NST2 | 267.91 | 278.21 | 293.21 | 303.52 | 316.58 | 326.89 | 343.24 | 353.54 | 355.45 | 365.75 | 368.36 | 378.66 | 372.34 | 382.64 | 402.64 | 412.95 |
NST3 | 266.28 | 274.52 | 294.24 | 302.48 | 318.28 | 326.53 | 345.13 | 353.37 | 355.92 | 364.16 | 367.89 | 376.14 | 370.65 | 378.89 | 407.10 | 415.34 |
NST4 | 266.38 | 274.63 | 291.73 | 299.97 | 314.99 | 323.23 | 343.10 | 351.35 | 366.55 | 374.80 | 370.38 | 378.62 | 402.20 | 410.44 | ||
NST5 | 266.47 | 274.71 | 292.00 | 300.25 | 315.20 | 323.44 | 343.23 | 351.47 | 353.98 | 362.22 | 366.65 | 374.89 | 370.41 | 378.65 | 400.50 | 408.74 |
ST | 265.05 | 271.23 | 293.03 | 299.21 | 316.45 | 322.63 | 345.93 | 352.11 | 355.04 | 361.22 | 366.06 | 372.24 | 368.66 | 374.84 | 407.17 | 413.35 |
Yozgat | ||||||||||||||||
NST1 | 269.93 | 280.05 | 305.29 | 315.42 | 333.99 | 344.12 | 360.89 | 371.02 | 373.02 | 383.14 | 394.05 | 404.17 | 417.14 | 427.27 | ||
NST2 | 269.86 | 279.99 | 305.21 | 315.34 | 333.89 | 344.02 | 360.29 | 370.42 | 371.74 | 381.87 | 391.79 | 401.92 | 394.08 | 404.20 | 414.81 | 424.94 |
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Oruc, S. Trend and nonstationary relation of extreme rainfall: Central Anatolia, Turkey. Acta Geophys. 69, 243–255 (2021). https://doi.org/10.1007/s11600-020-00518-w
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DOI: https://doi.org/10.1007/s11600-020-00518-w