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A frequency curve connects all values of the quantity for j = 1, n with the common property of equal probability of non-exceedance. Generally a group of curves is considered which represents specific points of the cumulative frequency distribution for each j. Let the frequency curves be represented by matrix BB~(k,j), (k = 1, nff~; j = 1, n) where nf is the number of frequencies for which curves are created, then values for Bk,j0 are obtained by linear interpolation:
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By considering all data Xi,j, i = 1, m and j = 1, n the average duration curve indicates how often a given level of the quantity considered will not be exceeded in a year (or month or day) on the average; note that this definition differs from the meaning of the 50% duration curve! Exceedance levels FR~k~ are obtained by partitioning the range between Xmax and Xmin into 30 parts.
Let Neff be the total number of data Xi,j > Xmin , where Neff ≤ m.n (depending on the number of missing data, and Nk the number of data not exceeding level FRk, then the average duration ADk of the event Xi,j ≤ FRk reads:
AD≤k≤ = (N≤k≤ /N≤eff≤).n
Duration curves
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By considering all data Xi,j ,i = 1,m and j = 1,n the average duration curve indicates how often a given level of the quantity considered will not be exceeded in a year (or month or day) on the average; note that this definition differs from the meaning of the 50% duration curve! Exceedance levels FRk are obtained by partitioning the range between Xmax and Xmin into 30 parts.
Let Neff be the total number of data Xi,j > Xmin, where Neff £m.n (depending on the number of missing data, and Nk the number of data not exceeding level FRk , then the average duration ADk of the event Xi,j £FR ≤ FRk reads:
ADk = (Nk /Neff ).n
Data requirements
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