International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Statistical investigation of extreme weather conditions Proske, D. Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  1Statistical Investigation of Extreme Weather Conditions D. Proske AXPO Power AG, Baden, Switzerland ABSTRACT: Structures are exposed to an ensemble of natural hazards. Earthquakes and flooding’s are the most recognized natural hazards, but structures also have to be safe under extreme weather condi-tions such wind and hurricanes, heat periods and colds, extreme rainfalls, hail and freezing rain. Some of this hazards are usually not investigated in detail, however based on statistical investigations, hazard curves and representative values of hazards can be defined, if required. They can be applied in proba-bilistic computations to achieve the probability of failure of the structures. Although major efforts have been undertaken in recent years to estimate the hazards and the representative values, we have to no-tice, that the validity of the provided natural hazards estimations by means of statistical investigations is limited due to confined sample populations. One of this causes is the recently increased knowledge using data with extreme values from non-instrumental periods, which heavily influences the outcome of the statistics, if considered. Newer statistical methods and the inclusion of historical data can, but need not necessarily improve results under all conditions. This development has also been observed in seismic loading estimation and in flooding hazard prognosis.  1. INTRODUCTION Structures are not only exposed to technical live and dead loads, they are also heavily exposed to natural loadings. Such loadings can reach ex-treme values, as known for seismic loading or flooding loads of water or sea exposed structures. However many other natural loadings exist, such as wind and storm loading, snow and ice loading, loadings from hail and rainfall or temperature loadings. Usually their contribution to the overall hazard figure is limited. Figure 1 shows the dif-ferent natural hazards for a structure in a relative size related to rough generic risk values. In the field of structural engineering, repre-sentative loading values for most hazards, such as wind and snow, have been developed and are based on statistical investigations (Handbuch Eurocode, but see also Lieberwirth 2003 and Proske & Van Gelder 2009). This studies mainly focus on the characteristic loading values with a return period of 50 years (98 % fractile), but some accidental loads are based on 10 000 year return period values (see Table 1). The allowed extrapolation time of statistics is in range of 3 to 4 of the covered observation time (Pugh 2004). This would yield to a required observation time of 2500 to 3300 years for the accidental load value. Of course, such measure-ment series do not exist. Therefore not only data from measurement times should be used, but also non-instrumental data. This development is cur-rently extended from seismic hazard assessment to all other natural hazards for structures.     Figure 1: Classification of several natural hazards. 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  2Table 1: Return periods of certain load combinations or load values(mainly based on Curbach & Proske 2002).  Load combination/ load value Return period  Quasi-static 50 percent of the time of the year Non-Frequent (DIN 1055) 1 day (300 times per year) Non-Frequent (DIN FB) 1 week Frequent 1 year Rare 10 years Characteristic (natural loading) 50 years Accidental (earthquake) 350 years Characteristic (traffic load) 1000 years Accidental load 10000 years  2. AVAILABLE DATA Observation periods for data can be distinguished into instrumental and non-instrumental periods. Non-instrumental periods can reach extreme times frames, for example in the field of seismic-ity. In Anatolia, based on geological investiga-tions, about 60 earthquakes over a certain magni-tude were identified for a time period of 4000 years (Gore 2000). Using written documents in some regions Mountain risk events can be identi-fied over a period of 2000 years. Non-instrumental data has been discussed so far in Austria and Switzerland for seismic haz-ards (Schwarz-Zanetti & Fäh 2011 a/b), for flooding (Tetzlaff et al. 2002, Wetter et al. 2011) and for Mountain risks (Totschnig & Hübl 2008, Disalp 2008). Many techniques exist for non-in-strumental data observations, for example bio-logical proxys, written documents, marks on structures and others (for an overview see Beh-ringer 2011). However in most cases, the accu-racy and density of the data points decreases, further one looks into the past.  In the last decades, climate history has pro-vided non-instrumental data for a variety of cli-matological parameters. This research was main-ly based on the discussion of climate change, see for example the discussion about Manns Stick. Results with different spatial resolutions mainly for Switzerland have been published by Pfister 1999, Behringer 2011, Dobrovolny et al. 2010, Ahmed et al. 2013, Z’graggen 2006. In many cases instrumental data is available for a certain time period, mainly in the region of years, decades and sometimes a century. First measurements of temperature range from the 18th century (Pfister 1999, Behringer 2011). For example, the measurement time series from Cen-tral England with daily data is available from 1772. However, local effects such as the color of neighboring houses, the type of the measurement device housing and other effects can change the maximum measured temperature up to 4 Kelvin (Z’graggen 2006). Therefore measurement data is nowadays intensively reviewed and checked (Füllemann et al. 2011, Begert et al. 2003, Begert et al. 2005). One can summarize: we need to extend our observation time, but quantity (see figure 2) and quality decrease looking further into the past. Both, instrumental and non-instrumental data include certain drawbacks.    Figure 2: Mountain risk events of several natural hazards (based on Totschnig & Hübl 2008) using non-instrumental data for the Salzburg region in Austria 3. STATISTICAL INVESTIGATIONS Major studies were undertaken to probabilistical-ly quantify natural hazards and to provide de-tailed information in Switzerland in the last dec-ade. For example, for seismic loading the PEGASOS and PRP Studies were carried out, running over more than 10 years. The studies are planned to reach the SSHAC Level 4 (Budnitz et 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  3al. 1997), the highest quality level on scientific seismic studies. The SSHAC (Senior Seismic Hazard Analysis Committee) gives rules and recommendations to provide seismic hazard es-timations. SSHAC level techniques spend major efforts to include uncertainty of data and meth-ods. Currently several SSHAC Level 3 projects are running worldwide (U.S. East cost study) to update and improve the quality of seismic hazard estimations. The same trend can be seen for flood hazard estimations, especially after some major floods occurred in central Europe in the last decade of the 20th century. Some flooding hazard analysis already in 2009 include historical data. Currently the PLATEX/EXAR (BAFU 2014) project is running in Switzerland, which uses comparable quality standards as used for the seismic study.  One of the latest projects in this frame is the project extreme weather conditions. In this pro-ject several extreme weather parameters have been investigated, such as rain, hail or snow. Again, studies have been carried out before, for example for the preparation of the SIA-codes. However in the latest study data from non-instrumental periods were heavily discussed. Besides that, extreme efforts were made during the statistical investigation. For example, for the rain data, the block maxima method was used and a generalized extreme value distribution was applied. The precipitation was investigated for seasonality, since rain shows maxima during the summer time. Therefore only data from May to September was used. Additionally to avoid time varying threshold levels, the distribution was used with time varying parameters. The fol-lowing seasonality trend was assumed in the fit-ting of the distribution:  Ljjj jtπsjtπcttμμtμ1010)365/2sin()365/2cos()()( (1) with μ(t) as statistical time depend parame-ter, here as mean value, μ0 as statistical parame-ter for a reference year, μ1 as linear trend of the statistical parameter, t as time, t0 as reference time (mainly in years) and cj and sj as constants for the consideration of seasonal variability. Both, shape and scale parameter of the gen-eralized extreme value distribution were adapted in the same way. Also the data was checked for annual changes over time.  Without going very much into detail, the above paragraph just shows the amount of deep-ness of the statistical analysis. Major efforts were undertaken to achieve robust and high quality hazard curves for the different hazards. 4. PROBLEMS Non-instrumental data should allow an extension of the data pool by including rare event data. However based on the rather low quality stand-ards for early measurements and the indirect in-dicators for non-measurement values, it is diffi-cult to merge both, data from instrumental and non-instrumental time periods in the field of ex-treme weather parameters. Whereas in flooding and seismic loading, extreme values are usually well documented by existing structures at the time of the event, for extreme temperatures non such evidence exists.  Unfortunately, mistakes and uncertainty of proxy-data can heavily influence all hazards and therefore all the results of the statistical inves-tigation. For example in Switzerland the intensity of the Lindau Earthquake from December 20 1720 was overestimated by a translation error from the original written documents. Also his-torical spatial relations can be misleading: an earthquake in the “Welschland” in 1152 was related to “Neuenburg” in Switzerland. However, the term „Welschland“ was not related to the French speaking Switzerland before the 19. cen-tury, but to Italy. Therefore the earthquake was related to a wrong location based on a wrong interpretation of written proxies. (Schwarz-Zanetti & Fäh 2011 a/b) In table 2 and figure 3 we try to visualize such problems. Figure 3 shows the temperature anomalies for Switzerland from 1444 to 2003 (Wetter & Pfister 2013). First of all, the devel-opment of this diagram is an excellent work. However, whether this diagram can be used for 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  4extreme temperature hazard estimation can be easily detected by the comparison of the results from the non-instrumental period with instru-mental data. Table 2 gives the official maximum temperature measurements for different locations in Switzerland. Based on table 2 the temperature anomaly in figure 3 for 2003 can be confirmed for the Swiss lowlands. However, the second largest temperature occurred for most measure-ments locations in 1983. In figure 3 the tempera-ture anomaly for 1983 is pretty close to the con-fidence range, but does not seem to be an ex-treme value. Even further, the 1983 temperature values are the maximum values in many temper-ature measurement data series for instrumental time periods. Furthermore for Basel, on of the longest temperature measurement data series (from 1864), the third largest measurement oc-curred in 1921, whereas in figure 3 the 1945- and the 1934-anomalies are extremer than the 1921 value.  One can summarize, the comparison of local temperature measurements with the reconstruc-tion of non-instrumental based temperature anomalies may be misleading. However, an solu-tion would be to create an spatial and temporal average, for example for the Swiss lowlands for three month, based on the local instrumental data series (this was partly done by Wetter & Pfister). After comparing this values for instrumental and non-instrumental periods, we could disassemble the anomalies from non-instrumental time to achieve local extreme values. Such comparisons show indeed, that in general spring temperatures increase in Switzerland. This explains the change of anomalies and the limitation of the annual maximum temperatures. This effects indicate, that data from non-instrumental periods require enormous proofing. Wetter & Pfister 2012 summarize in the discus-sion paper: “In summary, it is concluded that biological proxy data may not properly reveal record breaking heat and drought events in the pre-instrumental past. Obviously, such assess-ments need to be complemented with the critical study of contemporary documentary evidence being widespread in such situations and provid-ing coherent and detailed narratives about weath-er patterns and climate induced impacts.” How-ever, Totschnig & Hübl 2008 have also found major bias in written documents about historical events.   Table 2: Maximum annual temperatures in Switzer-land according to MeteoSwiss (Z’graggen 2006).  Station 2003 1983 1947 1921 Grono 41.5 1)    Locarno-Monti 37.9 37.3   Piotta 34.0 32.8   San Bernadino 27.6 27.9   Basel 38.6 2) 38.4 4)  38.4 4) Zürich 36.0 35.8 5) 35.8  Bern 37.0  35.9  Altdorf 36.5    Chateau d Oex  33.4 35.0   Gstaad-Grund 32.0 34.0   Adelbode 29.4 32.2   Mürren (1638 m)  30.4   Elm/ Engelberg 32.6 32.7   Napf 29.7 30.4   Pilatus 22.3 27.3   Gütsch o. Andermatt 22.8 25.1   Säntis 18.8 20.8   Sion 37.2    Ulrichen 30.5 32.2   Montana 30.0 30.6   Zermatt 30.1 31.9   Grächen 29.5 31.5   Chur 37.1 37.5   Disentis 32.6 32.9   Davos 27.3 29.0   Arosa 26.2 26.5   Weissfluhjoch 19.6 22.8   Sta. Maria 29.7 30.6   Robbia 32.9 33.3   Scuol 33.1    Genf 37.8   38.5  1) Record of Switzerland: Grono is located on the border to Italy 2) Record in the Northern Alp region 3) Value is challenged 4) 38.4°C from July 1983 and July 1921, the former maximum value was 39°C from July 2nd 1952, but was corrected to 37.3°C 5) The former maximum value of 37.7°C from July 29 1947 was corrected to 35.8 °C. 6) Foehn    12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  5  Figure 3: Temperature anomalies according to Wetter & Pfister 2013 for Switzerland   We can summarize, that instrumental data for the statistical estimation of extreme rare events is limited. The application of non-instru-mental data is difficult, since different methods (biological proxy, written documents) may yield to different results and the results may not be transferable to the appropriate climatological parameter (extreme daily air temperature versus temperature anomaly over several month, peak wind gust speed versus description of storm etc.). Furthermore longer time periods, although ade-quate for statistical extrapolation of extreme ac-cidental loads, may introduce changes of the population. The mentioned problems are not ob-served in this severity for seismic history, since here no change of population is assumed and geological artifacts are probably more robust than biological proxy’s. 5. SUMMARY The estimation of extreme rare events is required for design against accidental loads. Usually tradi-tional statistical methods are applied for the es-timation of the representative accidental loads. However, to extend the sample and observation time, the inclusion of non-instrumental data is currently state of the art (depending on the haz-ard type) to achieve accurate representative val-ues. Besides the application of statistics in the sense of Fisher, Bayesian update techniques can and have been used to include the rough data from non-instrumental periods.  However, increased understanding of histor-ical data (non-instrumental period) of extreme events may substantially change the results of the statistical investigation in rather short time peri-ods and therefore limiting the lifetime validity of the probabilistic computation. Furthermore, the historical data may also not belong to the same population (Little Ice Age) and requires further adaptation. Besides, as mentioned above, the investigation of non-instrumental data usually results in regional and seasonal averages, neither local values nor values with a high temporal granularity are available.  With this drawbacks in mind, we have to ac-cept, that the results of the statistical evaluation of extreme weather conditions using non-instru-mental data has limited validity. This confirms the application of the so-called integral risk cy-cle, which is widely applied for mountain risk engineering and living probabilistic safety as-sessments, which are common in Nuclear Engi-neering. The statement may jeopardize also the application of probabilistic methods in structural engineering, because it limits the lifetime of the results as mentioned above. We have to accept, 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  6that major loadings are permanently changing not only due to climate change, but also due to permanently increased knowledge about events in non-instrumental times. This brings us back to the question, whether a deterministic approach simply choosing an appropriate safety factor is more sufficient than a full probabilistic computa-tion. That is even further true, if we consider, that the design life time of structures is 50 or 100 years.  Whereas in Mountain risk engineering, im-provements in terms of debris flow barriers or rockfall protections nets can be installed after information update and repeated risk assessment, it seems to be impracticable to permanently re-construct houses simply by the sheer number of them. In Germany alone, about 23 million houses exist.  6. REFERENCES  Handbuch Eurocode 1 Einwirkungen, Band 1 bis 3, Beuth Verlag, Berlin, 06/2013 Lieberwirth, P.: Ein Beitrag zur Wind- und Schnee-lastmodellierung. 1. Dresdner Probabilistik-Symposium. Fakultät Bauingenieurwesen, Technische Universität Dresden. 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