where
(5)
1 l
bo = ∑ x(i)
l i =1
1 l i -1
b1 = ∑
x(i)
l i = 1l -1
(Wang 1991), where the x(i) are the ordered sample, x(1) x(2) ... x(l) of loads greater than the
threshold load u.
A variety of methods can be used to define the threshold load u. It should be high enough that
only true extremes are used to estimate the parameters of the GPD, but low enough that there are
sufficient data so sampling error is not a problem. Simiu and Heckert (1995) showed the varia-
tion in k with u for fastest-mile wind speed data. Some authors specify the threshold as a percen-
tile of the number of cases. For example, Walshaw (1994) used a threshold at about the 95th per-
centile of his 10 years of hourly maximum wind gusts. Sometimes the threshold is determined on
a physical basis (Abild et al. 1992).
Once the parameters of the distribution have been determined, the load xT corresponding to a
specified return period T is calculated from
xT = u +a [1 (lT)k ]/k,
(6)
where l is the occurrence rate (number per year) of storms exceeding the threshold load.
7.2 Superstations
The superstation concept is presented in Peterka (1992) for extreme wind speeds. The 50-
year return-period wind map in ASCE 7-88 showed small regions in the Midwest with high
winds. Peterka argued that these small-scale variations in the extreme wind speed were not real,
but were due to sampling error from determining the parameters of the extreme value distribution
from relatively short data records. He suggested that the records of extreme winds from different
weather stations with the same wind climate could be appended to each other to form a super-
station with a much longer period of record. This long period of record supplies many more
extremes to use in the extreme value analysis and thus produces better estimates of the parame-
ters of the extreme value distribution. For example, Peterka created a wind superstation that in-
cluded 29 stations in 11 states and had a 924-year period of record. The limitation on forming the
superstation was that the maximum annual winds from the different stations in the superstation
should be uncorrelated. If they are not, if the maximum annual wind speed in Cleveland, for
example, typically occurred in the same storm as the annual maximum in Cincinnati, then includ-
ing the second station supplies no new information on the extreme wind climate.
In forming the superstations for ice loads in this region we took into account the number of
severe ice storms at each station, the number of times adjacent stations were in the same severe
storm, the frequency of ice storms at each station, station elevation, latitude, proximity to water,
and relief. We attempted to balance grouping only stations likely to have the same icing climatol-
ogy against the desire to create superstations with as long periods of record as possible to reduce
sampling error. The weather stations used in the extreme value analysis were required to have
complete historical records of hourly weather data, including present weather, as well as either
hourly or 6-hourly precipitation amounts. Thus, we could not include data from CRREL (no
40
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