Changes in extreme sea-levels in the Baltic Sea

Sequence of annual maxima for Furuögrund (solid) and corresponding lowess smooth (dashed).

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Table 2. Likelihood ratio test (Q) for the null hypothesis (H ₀) of a Gumbel non-stationary model (ξ=0) and for a stationary model (β ₁=0)

Station nameQ(H₀: ξ=0)Q(H₀:β₁=0)

Gedser3.560.18Hornbæk3.300.72Kungsholmsfort0.065.36Ölands Norra Udde2.130.03Stockholm–3.49Ratan4.124.94Furuögrund1.4613.09

[i] For a 95% confidence level, H ₀ is rejected if Q>3.84 (values in bold).

Diagnostics plots: probability plot (left) and quantile-quantile plot (right) for the Furuögrund model.

Table 3. Maximum likelihood estimates for µ, σ and ξ of the selected models (standard errors in parentheses)

Station nameµ(mm)β₀ (mm)β₁ (mm)σ (mm)ξ

Gedser665.61 (15.66)140.66 (10.91)0Hornbæk696.69 (16.22)145.46 (11.43)0Kungsholmsfort428.61 (18.86)0.87 (0.35)91.61 (8.17)0Ölands Norra Udde485.07 (13.28)119.20 (9.55)0Stockholm384.74 (9.87)89.09 (7.54)0Ratan466.52 (37.38)1.87 (0.76)159.61 (13.20)−154.99 (70.64)Furuögrund467.10 (34.32)2.56 (0.66)154.42 (12.60)0

Table 4. Return levels (m) for 10, 25, 50 and 100 yr

Return levels (m)

Station10 yr25 yr50 yr100 yr

Gedser0.981.121.211.31Hornbæk1.021.161.261.37Kungsholmsfort0.640.730.790.86Ölands Norra Udde0.750.870.951.03Stockholm0.560.670.730.79Ratan0.770.870.941.00Furuögrund0.830.981.091.20

Quantile slopes (points) and corresponding standard errors (vertical error bars). The horizontal dashed line denotes the mean (0 mm/yr) trend.

Table 5. Quantile regression trends (standard errors in parentheses) and corresponding bootstrap estimates (ensemble median and IQR) for quantile 0.98

StationSlope (mm/yr)Ensemble median (mm/yr)

Gedser0.40* (0.22)0.40 (0.05)Hornbæk−0.04 (0.18)−0.04 (0.02)Kungsholmsfort1.20* (0.14)1.23 (0.06)Ölands NorraUdde1.04* (0.13)1.05 (0.07)Stockholm1.54* (0.15)1.55 (0.07)Ratan1.70* (0.12)1.74 (0.08)Furuögrund2.07* (0.14)2.10 (0.08)

[i] Statistically significant trends (95% confidence level) are denoted by *.

Table 6. Likelihood ratio test (Q) for the null hypothesis (H ₀) of a stationary GEV model (β ₁=0) for the atmospheric data

GridpointAir TSLPu-windv-wind

12.5°E 55.0°N3.130.822.010.6815.0°E 55.0°N2.590.96––17.5°E 55.0°N4.201.2220.5412.6520.0°E 55.0°N2.331.4916.3311.8717.5°E 57.5°N4.920.830.172.820.0°E 57.5°N2.271.0805.7620.0°E 60.0°N1.740.300.070.1620.0°E 62.5°N1.780.441.610.2922.5°E 65.0°N0.830.9815.755.70

[i] For a 95% confidence level, H ₀ is rejected if Q>3.84 (values in bold)

Table 7. Maximum likelihood estimates for the slope (β ₁) of the non-stationary GEV models (standard errors in parentheses)

Air Tu-windv-windGridpoint(°C/decade)(10⁻³ms⁻¹/yr)(10⁻³ms⁻¹/yr)

12.5°E 55.0°N–––15.0°E 55.0°N–––17.5°E 55.0°N0.28 (0.13)0.62 (0.0020)0.31 (0.0021)20.0°E 55.0°N–0.54 (0.0020)0.32 (0.0036)17.5°E 57.5°N0.22 (0.10)––20.0°E 57.5°N––0.31 (0.0020)20.0°E 60.0°N–––20.0°E 62.5°N–––22.5°E 65.0°N–0.30 (0.0020)0.21 (0.0045)

Table 8. Quantile regression trends (standard errors in parentheses) for quantile 0.98

Air TSLPu-windv-windGridpoint(°C/decade)mbar/yr(10⁻³ms⁻¹/yr)(10⁻³ms⁻¹/yr)

12.5°E 55.0°N0.17 (0.039)*0.035 (0.012)*0.28 (0.054)*0.076 (0.046)15.0°E 55.0°N0.14 (0.041)*0.042 (0.012)*0.42 (0.054)*0.081 (0.040)*17.5°E 55.0°N0.16 (0.041)*0.039 (0.011)*0.42 (0.059)*0.20 (0.038)*20.0°E 55.0°N0.16 (0.040)*0.048 (0.011)*0.33 (0.055)*0.21 (0.037)*17.5°E 57.5°N0.20 (0.036)*0.034 (0.012)*0.030 (0.058)−0.028 (0.050)20.0°E 57.5°N0.19 (0.035)*0.030 (0.013)*0.023 (0.063)−0.076 (0.052)20.0°E 60.0°N0.19 (0.031)*0.0067 (0.013)0.11 (0.051)*−0.0002 (0.051)20.0°E 62.5°N0.078 (0.037)*−0.011 (0.013)0.093 (0.045)*0.032 (0.043)22.5°E 65.0°N0.12 (0.028)*−0.025 (0.016)0.18 (0.051)*0.083 (0.04)*

[i] Statistically significant trends (95% confidence level) are denoted by *.

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DOI: https://doi.org/10.3402/tellusa.v66.20921 | Journal eISSN: 3035-9554

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Language: English

Page range: 20921 - 20921

Submitted on: Mar 22, 2013

Accepted on: Mar 18, 2014

Published on: Dec 1, 2014

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

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© 2014 Andreia Ribeiro, Susana M. Barbosa, Manuel G. Scotto, Reik V. Donner, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 66 (2014): Issue 1

Changes in extreme sea-levels in the Baltic Sea

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