## Results: Statistics |

To obtain a statistics report:

- From the select results form, select the
**statistics**result type. - Select the object and the variables of interest (see producing results).
- For frequency domain simulations, set the storm duration.
- Click the
**show**button.

The report is presented in a spreadsheet and is available for both time domain and frequency domain analyses.

- The minimum and maximum values and the simulation times when they occurred.
- The mean and standard deviation (i.e. the root mean square about the mean).

These statistics are reported for successive intervals of the simulation. If the **statistics by wave period** option is selected, then these intervals correspond to wave periods; otherwise they are the stages of the simulation.

Note: | Be careful when interpreting statistics of line clearance and seabed clearance, since these results are already minima – the shortest distance to any other line and to any point on the seabed. For example, the maximum of line contact clearance will be the maximum value that the smallest clearance took during the period. |

If a random wave analysis has been performed, results available are:

- The static value, calculated from the static state of the model, about which the dynamic part of the result is assumed to be a zero-mean stationary Gaussian process.
- The standard deviation of the result process.
- The most probable maximum (MPM) of the
*dynamic*part of the result process occurring in the storm duration, i.e. to find the total most probable maximum and minimum values the MPM must be added to and subtracted from the static value, respectively. - The mean period of zero up-crossings, $T_z$.
- The mean period of crests, $T_c$.
- The 0
^{th}, 1^{st}, 2^{nd}, 3^{rd}and 4^{th}moments of the spectral density. - The spectral bandwidth, $\epsilon$, of the result process.

If a regular wave analysis has been performed, results available are:

- The static value, calculated from the static state of the model.
- The standard deviation of the result, calculated from the amplitude, $a_r$, of the result as $\sigma_r = a_r / \sqrt{2}$
- The result amplitude and phase, reported as a lag from the wave elevation at the model's global origin.

Note: | For a regular wave analysis the loading is defined by a single regular wave, and because frequency domain results are calculated by applying a series of linear transforms, the result is a single harmonic. Hence the amplitude of the result is well-defined. |

This page reports an array of complex valued results process components defined as:

- Process index, identifies the independent process in which this component is contained. All components with the same index are from the same independent process. The lowest index value is always one.
- Process type, identifies the type of independent process in which this component is contained. It can be either wave, wind, or wave drift.
- Component frequency, is the temporal frequency the results process component is centred on.
- Component lower bound and upper bound, define the temporal frequency interval represented by the discrete component.
- Re and Im, are the real and imaginary parts of the complex result process component, $z_i$. The results process component is a harmonic with amplitude $\sqrt{2}|z_i|$ and phase lead $\arg(z_i)$.

The phase definition is dependent on the process type:

- For the wave process type, it is the phase lead relative to the wave component's crest at the global origin.
- For the wind process type, it is the phase lead relative to the wind component's peak velocity.
- For the wave drift process type, it does not define the phase lead relative to some physical feature of the environmental system, unlike the other process types. However, it allows the phase lead of the different results (or the same result at different model coordinates) to be defined relative to each other.