Extreme value analysis

As opposed to the 'normal' climate statistics, extreme value analysis focuses on the probability of (relatively) rare events. Rare events are the occurrence of extremely high waves or extremely strong winds. These extremes need not be present in the data samples: a Weibull curve is fitted to the data and used for extrapolation. Obviously, there exists a twilight zone between 'normal' and 'extreme' climate statistics.

Extreme value analysis addresses questions like

-During which fraction of the time will the waves exceed 10m?
-What is the return period of a storm in which the wind exceeds 30 m/s?
-What is the probability that a wave occurs higher than 20m in 25, 100 or 1000 years?

Waveclimate.com offers the possibility to express the fraction of time during which such a rare event occurs as the return period of storms with assumed average duration of 3, 6 or 12 hours. If we assume a typical storm duration of for instance 3 hours, while a storm with a wave above some extreme value is said to occur once every 1000 years, then the corresponding fraction of time would be 3/(1000*365*24).

The extreme value analysis screen lets you choose between two types of outputs available. It asks you to select

• The months of interest
• The variable to show (wave height or wind speed)
• The offshore data source (wave model or satellite)
• The type of output (fitted curve or fractile estimate)
• Additional settings for curve fitting

The months of interest

One or more specific months of interest can be selected to investigate seasonal variations in the climate. Typically, one may want to select the months of a particular season. If you do not know which months to choose, a monthly distribution may be helpful.

The variable to show

Extreme value statistics are available for wave height or wind speed. Wave height is significant wave height. Wind speed is wind speed at 10m above sealevel.

The offshore data source

Extreme value analysis can either be based on wave model data or satellite altimeter data. Wave model statistics are based on 3-hourly timeseries taken from the current grid point, being the grid point nearest to the current location.

We prefer satellites as data source for 'extreme' climate statistics.

The type of output

The fitted curve, also referred to as exceedance plot, is the primary type of output for extreme value analysis. A fitted curve shows the exceedance value or fractile as function of the fraction of time it is exceeded. These values are based on an extrapolation of Weibull curve that was fitted to the data above a given threshold. The second type of output, the fractile estimate, is complementary to the fitted curve: by showing the fractile that is exceeded during a fixed fraction of time as a function of the threshold, it helps to find the appropriate threshold.

The threshold applied for a fitted curve

Curves are fitted to the data above the specified threshold. For wind speed, the threshold is specified in m/s or in knots depending on the unit set in your preferences.

Additional settings for curve fitting

You are asked for two additional inputs concerning the curve fitting to be done for both exeedance and fractile estimate: the Weibull shape factor and the way in which the fraction of time will be expressed, also referred to as the fraction of time axis. The Weibull distribution, including the shape factor, is used to extrapolate beyond the maximum value observed, and to calculate the chance that some extreme value is exceeded. By taking different samples from the data set, the reliability of this extrapolation can be estimated. The fraction of time quantity relates to the length of events (storms) and influences curve fitting done for both the exceedance plot and the threshold sensitivity plot

Tip: Refer to the related FAQ on how to choose the input parameters for extreme value analysis.

Tip: Background and guidelines for extreme value analysis are also available as Word document.

Tip: Logon as demo (no password needed) to get acquainted with the different types of output without being charged.