EM 1110-2-1100 (Part II)
30 Apr 02
Definition of Short-Term and Long-Term Statistics
Typical Time Period
Variations within an individual sea state
Variations over a long-term collection of sea states
c. Statistical parameters. For most design applications, it is sufficient to represent a sea state by a few
parameters. A mean value usually suffices for most processes, such as water level, current, wind speed, and
direction. Wave parameters require special consideration (see Part II-1). Typically the parameters Hm0, Tp,
and θp are used to represent either the total sea state or each major wave component in the sea state, which
may include a locally generated sea and several independent swell components. It is especially important to
note in shallow water design applications that the energy-based parameter Hm0 and the height-based parameter
H1/3 may differ substantially (see Part II-1). Wave height is often the most critical design parameter and the
choice of parameter must be consistent with the particular design application. For example, Hm0 is appropriate
for sediment transport and beach erosion applications, but H1/3, H10, or H1 may be preferred for estimating
wave forces on a pier.
II-8-5. Statistical Methods - Long-term
(1) Statistical methods for analyzing long-term information covering many years are an integral part of
most design applications. These methods deal with the various values assumed by selected statistical
parameters representing short-term information. Typically the largest parameter values are the primary design
concern. For example, the largest value of the statistical parameter Hm0 to be expected over a 25-year time
interval might be needed.
(2) Extreme events are often highly variable in terms of intensity and sequencing. By definition, they
are rare. Thus, long-term statistical methods must deal with the problem of using a small, variable sample
to estimate parameters that often have a major impact on design. Engineers are continually reminded that
events such as the 100-year extreme storm can by chance occur during a much shorter data collection effort.
Conversely, a 10-year record may not contain any events that equal or exceed the long-term 10-year extreme.
Long-term statistical methods typically address the following two, related problems:
(a) How to extend available information to a longer time period; e.g., how to use 10 years of data to
estimate the 25-year extreme.
(b) How to use a small sample of extreme events to get unbiased extreme estimates and some measure
of confidence or variability that can be expected in the estimates.
(3) In some applications, the preferred approach is to extend the available information base to longer time
periods by generating additional realizations of the process and ensuring that the realizations are statistically
consistent with known information. One adaptation of this approach is described in the following section on
stochastic time histories.
Hydrodynamic Analysis and Design Conditions