Input Data. The input data must meet two conditions: homogeneity and independence. A homogeneity issue has two faces: (1) absence of trend; (2) a common parent probability distribution, which may be considered for granted within a common synoptic mechanism. To provide the latter, each synoptic mechanism dataset is to be treated separately. For each station, its input dataset included two highest 10-minute wind speed values for each valid wind year for each synoptic mechanism. A wind year for the Eastern Mediterranean is established from September, 1 to August, 31. A wind year is considered valid if there are no missing data during the windiest events. The EWT has an option of switching between using the one-maximum-per-year or two-maxima-per-year dataset. When a number of valid wind years is 10 or more, a one-maximum option is used. Otherwise, the algorithm switches to a two-maxima dataset.
Preprocessing. (A) The 10-minute wind-speed records over 1999-2017 has been divided into the separated synoptic events using objective and manual techniques. Given a small size of Israel, the common synoptic-event division has been applied to all stations. (B) For each synoptic event, a maximum wind speed for each one of the 12 wind-direction sectors has been fixed with the corresponding directional roughness and orography coefficients specific for each station, and the highest one has been defined as a maximum wind speed per event. (C) For each wind year and for each one of 5 synoptic mechanism, two annual maxima has been selected.
The EWT included several steps as follow:
Step 1. Stability Check. The von Neumann homogeneity test has been applied to each dataset for finding a trend. As a rule, the stronger a synoptic mechanism the more stable the corresponding wind speed annual maximum time-series. The synoptic mechanisms producing weak winds are out of interests, for their contribution in the final high quantile estimation is negligible. All stations but one showed no trend in the annual wind speed maximum for their corresponding major synoptic mechanism. A station with trend would be excluded from participating in mapping. Since the von Neumann test is to be applied to the normal distributed data, a normality has been tested as well.
Step 2. Estimating the Extreme Value Distribution Parameters. The Gumbel, or Extreme Value Type I Distribution EVD is commonly applied for estimating the extreme wind speed. Here, four methods of estimating the EVD parameters are being compared: BLUE - Best Linear Unbiased Estimation, MOM - Method of Moments, LMOM - Linear combination of Moments, and MLE – Maximum Likelihood Estimation. The critical values are being calculated with the Modified Anderson-Darling goodness-of-fit test for the upper tail, AU2. We used the AU2 original formula, with the Hazen's empirical CDF plotting positions PP, and in addition, reformulated it with the Weibull's PP. These are two opposite PP approaches among all suggested in the related literature. Thus, we could evaluate the possible effects of selecting a PP approach on the p-value estimates. The latter were obtained with the pre-calculated critical value tables built with the Monte-Carlo simulations for both Hazen's and Weibull's PP.
Step 3. Selecting the Optimal Estimating Method. To get to consistent mapping, one common method is to be selected for all stations and for all synoptic mechanisms. The comparison of the p-values boxplots with 71 data in each showed that for the leading synoptic mechanisms, the BLUE method was the best, immediately followed by the LMOM. In final calculations, the common method of BLUE was applied for the EVD parameters' estimating for all synoptic mechanisms for all stations.
Step 4. Calculating the Final Extreme Wind Quantiles. For each stations, for each synoptic mechanism, the estimated EVD parameters were applied to calculate the CDF corresponding to each wind speed ws from 10 to 50 m/s with a step of 0.1 m/s. Since all synoptic mechanisms are mutual-exclusive, the total CDF for each ws was easily calculated analytically. Combining the total CDF for all ws, we obtained the final CDF as a function of wind speed. Then, the desired 50-year, 100-year, 200-year and so on quantiles, which correspond to 98%, 99%, 99.5% and so on, has been calculated numerically from the final CDF. In the same way, the confidence bounds, built with the bootstrap method for each synoptic mechanism, has been combined analytically into the confidence bounds of the total CDF.
Comparison Estimating Methods by Mapping. To be more confident about selecting the best method, we mapped the 50-year wind-speed quantiles for all stations with both the BLUE and LMOM methods. The BLUE map looked more homogeneous over the specific regions of the country, so the BLUE method was eventually defined as the best one.
Refs:
NIST, 2018, Special-Purpose Software: BLUE Extreme Value Type I Estimation, https://www.itl.nist.gov/div898/winds/gumbel_blue/gumbblue.htm
JP Palutikof, BB Brabson, DH Lister and ST Adcock, 1999. A review of methods to calculate extreme wind speeds. Meteorol. Appl. 6, 119–132.
H Shin, Y Jung, C Jeong and J-H Heo, 2011. Assessment of modified Anderson–Darling test statistics for the generalized extreme value and generalized logistic distributions. Stochastic Environmental Research and Risk Assessment, DOI 10.1007/s00477-011-0463-y
- Indicates paper has been withdrawn from meeting
- Indicates an Award Winner